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Simplifying 3x(2 + -1x) + -5x(7 + 2x) = 10 + -4x + 5 (2 * 3x + -1x * 3x) + -5x(7 + 2x) = 10 + -4x + 5 (6x + -3x2) + -5x(7 + 2x) = 10 + -4x + 5 6x + -3x2 + (7 * -5x + 2x * -5x) = 10 + -4x + 5 6x + -3x2 + (-35x + -10x2) = 10 + -4x + 5 Reorder the terms: 6x + -35x + -3x2 + -10x2 = 10 + -4x + 5 Combine like terms: 6x + -35x = -29x -29x + -3x2 + -10x2 = 10 + -4x + 5 Combine like terms: -3x2 + -10x2 = -13x2 -29x + -13x2 = 10 + -4x + 5 Reorder the terms: -29x + -13x2 = 10 + 5 + -4x Combine like terms: 10 + 5 = 15 -29x + -13x2 = 15 + -4x Solving -29x + -13x2 = 15 + -4x Solving for variable 'x'. Reorder the terms: -15 + -29x + 4x + -13x2 = 15 + -4x + -15 + 4x Combine like terms: -29x + 4x = -25x -15 + -25x + -13x2 = 15 + -4x + -15 + 4x Reorder the terms: -15 + -25x + -13x2 = 15 + -15 + -4x + 4x Combine like terms: 15 + -15 = 0 -15 + -25x + -13x2 = 0 + -4x + 4x -15 + -25x + -13x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -15 + -25x + -13x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 25x + 13x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 25x + 13x2)' equal to zero and attempt to solve: Simplifying 15 + 25x + 13x2 = 0 Solving 15 + 25x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 1.153846154 + 1.923076923x + x2 = 0 Move the constant term to the right: Add '-1.153846154' to each side of the equation. 1.153846154 + 1.923076923x + -1.153846154 + x2 = 0 + -1.153846154 Reorder the terms: 1.153846154 + -1.153846154 + 1.923076923x + x2 = 0 + -1.153846154 Combine like terms: 1.153846154 + -1.153846154 = 0.000000000 0.000000000 + 1.923076923x + x2 = 0 + -1.153846154 1.923076923x + x2 = 0 + -1.153846154 Combine like terms: 0 + -1.153846154 = -1.153846154 1.923076923x + x2 = -1.153846154 The x term is 1.923076923x. Take half its coefficient (0.9615384615). Square it (0.9245562129) and add it to both sides. Add '0.9245562129' to each side of the equation. 1.923076923x + 0.9245562129 + x2 = -1.153846154 + 0.9245562129 Reorder the terms: 0.9245562129 + 1.923076923x + x2 = -1.153846154 + 0.9245562129 Combine like terms: -1.153846154 + 0.9245562129 = -0.2292899411 0.9245562129 + 1.923076923x + x2 = -0.2292899411 Factor a perfect square on the left side: (x + 0.9615384615)(x + 0.9615384615) = -0.2292899411 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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