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Simplifying 2x(x + -6) + -3(2x + -5) = 0 Reorder the terms: 2x(-6 + x) + -3(2x + -5) = 0 (-6 * 2x + x * 2x) + -3(2x + -5) = 0 (-12x + 2x2) + -3(2x + -5) = 0 Reorder the terms: -12x + 2x2 + -3(-5 + 2x) = 0 -12x + 2x2 + (-5 * -3 + 2x * -3) = 0 -12x + 2x2 + (15 + -6x) = 0 Reorder the terms: 15 + -12x + -6x + 2x2 = 0 Combine like terms: -12x + -6x = -18x 15 + -18x + 2x2 = 0 Solving 15 + -18x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -9x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -9x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -9x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -9x + x2 = 0 + -7.5 -9x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -9x + x2 = -7.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -7.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -7.5 + 20.25 Combine like terms: -7.5 + 20.25 = 12.75 20.25 + -9x + x2 = 12.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x + -4.5) equal to 3.570714214 and -3.570714214.Subproblem 1
x + -4.5 = 3.570714214 Simplifying x + -4.5 = 3.570714214 Reorder the terms: -4.5 + x = 3.570714214 Solving -4.5 + x = 3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 3.570714214 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.570714214 + 4.5 x = 3.570714214 + 4.5 Combine like terms: 3.570714214 + 4.5 = 8.070714214 x = 8.070714214 Simplifying x = 8.070714214Subproblem 2
x + -4.5 = -3.570714214 Simplifying x + -4.5 = -3.570714214 Reorder the terms: -4.5 + x = -3.570714214 Solving -4.5 + x = -3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -3.570714214 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.570714214 + 4.5 x = -3.570714214 + 4.5 Combine like terms: -3.570714214 + 4.5 = 0.929285786 x = 0.929285786 Simplifying x = 0.929285786Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.070714214, 0.929285786}
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