[size=150]What number should be added to the expression [math]x^2-15x[/math] to result in an expression equivalent to a perfect square?[/size]
[size=100]Noah uses the quadratic formula to solve the equation [math]2x^2+3x-5=4[/math]. He finds [math]x=\text{-}2.5[/math] or [math]1[/math]. But, when he checks his answer, he finds that neither -2.5 nor 1 are solutions to the equation. [br]Here are his steps:[/size][br][math]a=2[/math], [math]b=3[/math], [math]c=\text{-}5[/math][br][math]x=\frac{\text{-}3\pm\sqrt{3^2-4\cdot2\cdot\text{-}5}}{2\cdot2}[/math][br][math]x=\frac{\text{-}3\pm\sqrt{49}}{4}[/math][br][math]x=\text{-}2.5[/math] or [math]1[/math][br][br]Explain what Noah’s mistake was.[br]
Solve the equation correctly.[br]
[math]x^2-2x=\text{-}1[/math]
[math]x^2+8x+14=23[/math]
[size=150]What are the solutions to the equation [math]x^2-4x=\text{-}3[/math]?[/size]
[size=150]Which expression is equivalent to [math]\sqrt{\text{-}23}[/math]?[/size]
[size=150]Write each expression in the form [math]a+bi[/math], where [math]a[/math] and [math]b[/math] are real numbers.[/size][br][br][math]5i^2[/math]
[math]i^2\cdot i^2[/math]
[math](\text{-}3i)^2[/math]
[math](5+4i)-(\text{-}3+2i)[/math]
[size=150]Let [math]m=(7-2i)[/math] and [math]k=3i[/math]. Write each expression in the form [math]a+bi[/math], where [math]a[/math] and [math]b[/math] are real numbers.[br][/size][br][math]k-m[/math]