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Simplifying 6 + -2x(x + 6) = 3x + 4 Reorder the terms: 6 + -2x(6 + x) = 3x + 4 6 + (6 * -2x + x * -2x) = 3x + 4 6 + (-12x + -2x2) = 3x + 4 Reorder the terms: 6 + -12x + -2x2 = 4 + 3x Solving 6 + -12x + -2x2 = 4 + 3x Solving for variable 'x'. Reorder the terms: 6 + -4 + -12x + -3x + -2x2 = 4 + 3x + -4 + -3x Combine like terms: 6 + -4 = 2 2 + -12x + -3x + -2x2 = 4 + 3x + -4 + -3x Combine like terms: -12x + -3x = -15x 2 + -15x + -2x2 = 4 + 3x + -4 + -3x Reorder the terms: 2 + -15x + -2x2 = 4 + -4 + 3x + -3x Combine like terms: 4 + -4 = 0 2 + -15x + -2x2 = 0 + 3x + -3x 2 + -15x + -2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 2 + -15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + 7.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 7.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 7.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 7.5x + x2 = 0 + 1 7.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 7.5x + x2 = 1 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 1 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 1 + 14.0625 Combine like terms: 1 + 14.0625 = 15.0625 14.0625 + 7.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + 3.75) equal to 3.881043674 and -3.881043674.Subproblem 1
x + 3.75 = 3.881043674 Simplifying x + 3.75 = 3.881043674 Reorder the terms: 3.75 + x = 3.881043674 Solving 3.75 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 3.881043674 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 3.881043674 + -3.75 x = 3.881043674 + -3.75 Combine like terms: 3.881043674 + -3.75 = 0.131043674 x = 0.131043674 Simplifying x = 0.131043674Subproblem 2
x + 3.75 = -3.881043674 Simplifying x + 3.75 = -3.881043674 Reorder the terms: 3.75 + x = -3.881043674 Solving 3.75 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -3.881043674 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -3.881043674 + -3.75 x = -3.881043674 + -3.75 Combine like terms: -3.881043674 + -3.75 = -7.631043674 x = -7.631043674 Simplifying x = -7.631043674Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.131043674, -7.631043674}
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