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Simplifying 2 + -6x(4x + 5) + 10 = 5x Reorder the terms: 2 + -6x(5 + 4x) + 10 = 5x 2 + (5 * -6x + 4x * -6x) + 10 = 5x 2 + (-30x + -24x2) + 10 = 5x Reorder the terms: 2 + 10 + -30x + -24x2 = 5x Combine like terms: 2 + 10 = 12 12 + -30x + -24x2 = 5x Solving 12 + -30x + -24x2 = 5x Solving for variable 'x'. Reorder the terms: 12 + -30x + -5x + -24x2 = 5x + -5x Combine like terms: -30x + -5x = -35x 12 + -35x + -24x2 = 5x + -5x Combine like terms: 5x + -5x = 0 12 + -35x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -0.5 + 1.458333333x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.458333333x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.458333333x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.458333333x + x2 = 0 + 0.5 1.458333333x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.458333333x + x2 = 0.5 The x term is 1.458333333x. Take half its coefficient (0.7291666665). Square it (0.5316840275) and add it to both sides. Add '0.5316840275' to each side of the equation. 1.458333333x + 0.5316840275 + x2 = 0.5 + 0.5316840275 Reorder the terms: 0.5316840275 + 1.458333333x + x2 = 0.5 + 0.5316840275 Combine like terms: 0.5 + 0.5316840275 = 1.0316840275 0.5316840275 + 1.458333333x + x2 = 1.0316840275 Factor a perfect square on the left side: (x + 0.7291666665)(x + 0.7291666665) = 1.0316840275 Calculate the square root of the right side: 1.015718478 Break this problem into two subproblems by setting (x + 0.7291666665) equal to 1.015718478 and -1.015718478.Subproblem 1
x + 0.7291666665 = 1.015718478 Simplifying x + 0.7291666665 = 1.015718478 Reorder the terms: 0.7291666665 + x = 1.015718478 Solving 0.7291666665 + x = 1.015718478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7291666665' to each side of the equation. 0.7291666665 + -0.7291666665 + x = 1.015718478 + -0.7291666665 Combine like terms: 0.7291666665 + -0.7291666665 = 0.0000000000 0.0000000000 + x = 1.015718478 + -0.7291666665 x = 1.015718478 + -0.7291666665 Combine like terms: 1.015718478 + -0.7291666665 = 0.2865518115 x = 0.2865518115 Simplifying x = 0.2865518115Subproblem 2
x + 0.7291666665 = -1.015718478 Simplifying x + 0.7291666665 = -1.015718478 Reorder the terms: 0.7291666665 + x = -1.015718478 Solving 0.7291666665 + x = -1.015718478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7291666665' to each side of the equation. 0.7291666665 + -0.7291666665 + x = -1.015718478 + -0.7291666665 Combine like terms: 0.7291666665 + -0.7291666665 = 0.0000000000 0.0000000000 + x = -1.015718478 + -0.7291666665 x = -1.015718478 + -0.7291666665 Combine like terms: -1.015718478 + -0.7291666665 = -1.7448851445 x = -1.7448851445 Simplifying x = -1.7448851445Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2865518115, -1.7448851445}
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