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Simplifying 5x(9 + -1x) = 37.5 (9 * 5x + -1x * 5x) = 37.5 (45x + -5x2) = 37.5 Solving 45x + -5x2 = 37.5 Solving for variable 'x'. Reorder the terms: -37.5 + 45x + -5x2 = 37.5 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 -37.5 + 45x + -5x2 = 0.0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 7.5 + -9x + x2 = 0.0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -9x + -7.5 + x2 = 0.0 + -7.5 Reorder the terms: 7.5 + -7.5 + -9x + x2 = 0.0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -9x + x2 = 0.0 + -7.5 -9x + x2 = 0.0 + -7.5 Combine like terms: 0.0 + -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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