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Simplifying 4x2 + -9x2 + -36x + -14 = 0 Reorder the terms: -14 + -36x + 4x2 + -9x2 = 0 Combine like terms: 4x2 + -9x2 = -5x2 -14 + -36x + -5x2 = 0 Solving -14 + -36x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 36x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + 36x + 5x2)' equal to zero and attempt to solve: Simplifying 14 + 36x + 5x2 = 0 Solving 14 + 36x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.8 + 7.2x + x2 = 0 Move the constant term to the right: Add '-2.8' to each side of the equation. 2.8 + 7.2x + -2.8 + x2 = 0 + -2.8 Reorder the terms: 2.8 + -2.8 + 7.2x + x2 = 0 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + 7.2x + x2 = 0 + -2.8 7.2x + x2 = 0 + -2.8 Combine like terms: 0 + -2.8 = -2.8 7.2x + x2 = -2.8 The x term is 7.2x. Take half its coefficient (3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. 7.2x + 12.96 + x2 = -2.8 + 12.96 Reorder the terms: 12.96 + 7.2x + x2 = -2.8 + 12.96 Combine like terms: -2.8 + 12.96 = 10.16 12.96 + 7.2x + x2 = 10.16 Factor a perfect square on the left side: (x + 3.6)(x + 3.6) = 10.16 Calculate the square root of the right side: 3.18747549 Break this problem into two subproblems by setting (x + 3.6) equal to 3.18747549 and -3.18747549.Subproblem 1
x + 3.6 = 3.18747549 Simplifying x + 3.6 = 3.18747549 Reorder the terms: 3.6 + x = 3.18747549 Solving 3.6 + x = 3.18747549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = 3.18747549 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = 3.18747549 + -3.6 x = 3.18747549 + -3.6 Combine like terms: 3.18747549 + -3.6 = -0.41252451 x = -0.41252451 Simplifying x = -0.41252451Subproblem 2
x + 3.6 = -3.18747549 Simplifying x + 3.6 = -3.18747549 Reorder the terms: 3.6 + x = -3.18747549 Solving 3.6 + x = -3.18747549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = -3.18747549 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = -3.18747549 + -3.6 x = -3.18747549 + -3.6 Combine like terms: -3.18747549 + -3.6 = -6.78747549 x = -6.78747549 Simplifying x = -6.78747549Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.41252451, -6.78747549}Solution
x = {-0.41252451, -6.78747549}
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