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Simplifying 10x2 + 90x + 75 = 0 Reorder the terms: 75 + 90x + 10x2 = 0 Solving 75 + 90x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(15 + 18x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(15 + 18x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + 18x + 2x2 = 0 Solving 15 + 18x + 2x2 = 0 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 = -0.929285786 x = -0.929285786 Simplifying x = -0.929285786Subproblem 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 = -8.070714214 x = -8.070714214 Simplifying x = -8.070714214Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.929285786, -8.070714214}Solution
x = {-0.929285786, -8.070714214}
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