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Simplifying 15x2 + -165x = -630 Reorder the terms: -165x + 15x2 = -630 Solving -165x + 15x2 = -630 Solving for variable 'x'. Reorder the terms: 630 + -165x + 15x2 = -630 + 630 Combine like terms: -630 + 630 = 0 630 + -165x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(42 + -11x + x2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(42 + -11x + x2)' equal to zero and attempt to solve: Simplifying 42 + -11x + x2 = 0 Solving 42 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -11x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + -11x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -11x + x2 = 0 + -42 -11x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 -11x + x2 = -42 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -42 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -42 + 30.25 Combine like terms: -42 + 30.25 = -11.75 30.25 + -11x + x2 = -11.75 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = -11.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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