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Simplifying x = 2(x + 10)(3x + -30) Reorder the terms: x = 2(10 + x)(3x + -30) Reorder the terms: x = 2(10 + x)(-30 + 3x) Multiply (10 + x) * (-30 + 3x) x = 2(10(-30 + 3x) + x(-30 + 3x)) x = 2((-30 * 10 + 3x * 10) + x(-30 + 3x)) x = 2((-300 + 30x) + x(-30 + 3x)) x = 2(-300 + 30x + (-30 * x + 3x * x)) x = 2(-300 + 30x + (-30x + 3x2)) Combine like terms: 30x + -30x = 0 x = 2(-300 + 0 + 3x2) x = 2(-300 + 3x2) x = (-300 * 2 + 3x2 * 2) x = (-600 + 6x2) Solving x = -600 + 6x2 Solving for variable 'x'. Reorder the terms: 600 + x + -6x2 = -600 + 6x2 + 600 + -6x2 Reorder the terms: 600 + x + -6x2 = -600 + 600 + 6x2 + -6x2 Combine like terms: -600 + 600 = 0 600 + x + -6x2 = 0 + 6x2 + -6x2 600 + x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 600 + x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -100 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -0.1666666667x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -0.1666666667x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -0.1666666667x + x2 = 0 + 100 -0.1666666667x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -0.1666666667x + x2 = 100 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1666666667x + 0.25 + x2 = 100 + 0.25 Reorder the terms: 0.25 + -0.1666666667x + x2 = 100 + 0.25 Combine like terms: 100 + 0.25 = 100.25 0.25 + -0.1666666667x + x2 = 100.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + 0.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + 0.5 = 10.012492197 Simplifying x + 0.5 = 10.012492197 Reorder the terms: 0.5 + x = 10.012492197 Solving 0.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.012492197 + -0.5 x = 10.012492197 + -0.5 Combine like terms: 10.012492197 + -0.5 = 9.512492197 x = 9.512492197 Simplifying x = 9.512492197Subproblem 2
x + 0.5 = -10.012492197 Simplifying x + 0.5 = -10.012492197 Reorder the terms: 0.5 + x = -10.012492197 Solving 0.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.012492197 + -0.5 x = -10.012492197 + -0.5 Combine like terms: -10.012492197 + -0.5 = -10.512492197 x = -10.512492197 Simplifying x = -10.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.512492197, -10.512492197}
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