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Simplifying -3(5x2 + 2x + 9) + x(2x + -3) = 0 Reorder the terms: -3(9 + 2x + 5x2) + x(2x + -3) = 0 (9 * -3 + 2x * -3 + 5x2 * -3) + x(2x + -3) = 0 (-27 + -6x + -15x2) + x(2x + -3) = 0 Reorder the terms: -27 + -6x + -15x2 + x(-3 + 2x) = 0 -27 + -6x + -15x2 + (-3 * x + 2x * x) = 0 -27 + -6x + -15x2 + (-3x + 2x2) = 0 Reorder the terms: -27 + -6x + -3x + -15x2 + 2x2 = 0 Combine like terms: -6x + -3x = -9x -27 + -9x + -15x2 + 2x2 = 0 Combine like terms: -15x2 + 2x2 = -13x2 -27 + -9x + -13x2 = 0 Solving -27 + -9x + -13x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(27 + 9x + 13x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(27 + 9x + 13x2)' equal to zero and attempt to solve: Simplifying 27 + 9x + 13x2 = 0 Solving 27 + 9x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 2.076923077 + 0.6923076923x + x2 = 0 Move the constant term to the right: Add '-2.076923077' to each side of the equation. 2.076923077 + 0.6923076923x + -2.076923077 + x2 = 0 + -2.076923077 Reorder the terms: 2.076923077 + -2.076923077 + 0.6923076923x + x2 = 0 + -2.076923077 Combine like terms: 2.076923077 + -2.076923077 = 0.000000000 0.000000000 + 0.6923076923x + x2 = 0 + -2.076923077 0.6923076923x + x2 = 0 + -2.076923077 Combine like terms: 0 + -2.076923077 = -2.076923077 0.6923076923x + x2 = -2.076923077 The x term is 0.6923076923x. Take half its coefficient (0.3461538462). Square it (0.1198224852) and add it to both sides. Add '0.1198224852' to each side of the equation. 0.6923076923x + 0.1198224852 + x2 = -2.076923077 + 0.1198224852 Reorder the terms: 0.1198224852 + 0.6923076923x + x2 = -2.076923077 + 0.1198224852 Combine like terms: -2.076923077 + 0.1198224852 = -1.9571005918 0.1198224852 + 0.6923076923x + x2 = -1.9571005918 Factor a perfect square on the left side: (x + 0.3461538462)(x + 0.3461538462) = -1.9571005918 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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