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Simplifying -2x(x + -6) = -3(x + 4) + -9 Reorder the terms: -2x(-6 + x) = -3(x + 4) + -9 (-6 * -2x + x * -2x) = -3(x + 4) + -9 (12x + -2x2) = -3(x + 4) + -9 Reorder the terms: 12x + -2x2 = -3(4 + x) + -9 12x + -2x2 = (4 * -3 + x * -3) + -9 12x + -2x2 = (-12 + -3x) + -9 Reorder the terms: 12x + -2x2 = -12 + -9 + -3x Combine like terms: -12 + -9 = -21 12x + -2x2 = -21 + -3x Solving 12x + -2x2 = -21 + -3x Solving for variable 'x'. Reorder the terms: 21 + 12x + 3x + -2x2 = -21 + -3x + 21 + 3x Combine like terms: 12x + 3x = 15x 21 + 15x + -2x2 = -21 + -3x + 21 + 3x Reorder the terms: 21 + 15x + -2x2 = -21 + 21 + -3x + 3x Combine like terms: -21 + 21 = 0 21 + 15x + -2x2 = 0 + -3x + 3x 21 + 15x + -2x2 = -3x + 3x Combine like terms: -3x + 3x = 0 21 + 15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -10.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -7.5x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -7.5x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -7.5x + x2 = 0 + 10.5 -7.5x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -7.5x + x2 = 10.5 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 = 10.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 10.5 + 14.0625 Combine like terms: 10.5 + 14.0625 = 24.5625 14.0625 + -7.5x + x2 = 24.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 24.5625 Calculate the square root of the right side: 4.9560569 Break this problem into two subproblems by setting (x + -3.75) equal to 4.9560569 and -4.9560569.Subproblem 1
x + -3.75 = 4.9560569 Simplifying x + -3.75 = 4.9560569 Reorder the terms: -3.75 + x = 4.9560569 Solving -3.75 + x = 4.9560569 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 = 4.9560569 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.9560569 + 3.75 x = 4.9560569 + 3.75 Combine like terms: 4.9560569 + 3.75 = 8.7060569 x = 8.7060569 Simplifying x = 8.7060569Subproblem 2
x + -3.75 = -4.9560569 Simplifying x + -3.75 = -4.9560569 Reorder the terms: -3.75 + x = -4.9560569 Solving -3.75 + x = -4.9560569 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 = -4.9560569 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.9560569 + 3.75 x = -4.9560569 + 3.75 Combine like terms: -4.9560569 + 3.75 = -1.2060569 x = -1.2060569 Simplifying x = -1.2060569Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.7060569, -1.2060569}
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