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Simplifying 9x2 + 15x + c = 20 + c Reorder the terms: c + 15x + 9x2 = 20 + c Add '-1c' to each side of the equation. c + 15x + -1c + 9x2 = 20 + c + -1c Reorder the terms: c + -1c + 15x + 9x2 = 20 + c + -1c Combine like terms: c + -1c = 0 0 + 15x + 9x2 = 20 + c + -1c 15x + 9x2 = 20 + c + -1c Combine like terms: c + -1c = 0 15x + 9x2 = 20 + 0 15x + 9x2 = 20 Solving 15x + 9x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 15x + 9x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 15x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 1.666666667x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 1.666666667x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 2.222222222 1.666666667x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 1.666666667x + x2 = 2.222222222 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 2.222222222 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 2.222222222 + 0.6944444447 Combine like terms: 2.222222222 + 0.6944444447 = 2.9166666667 0.6944444447 + 1.666666667x + x2 = 2.9166666667 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 2.9166666667 Calculate the square root of the right side: 1.707825128 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.707825128 and -1.707825128.Subproblem 1
x + 0.8333333335 = 1.707825128 Simplifying x + 0.8333333335 = 1.707825128 Reorder the terms: 0.8333333335 + x = 1.707825128 Solving 0.8333333335 + x = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.707825128 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.707825128 + -0.8333333335 x = 1.707825128 + -0.8333333335 Combine like terms: 1.707825128 + -0.8333333335 = 0.8744917945 x = 0.8744917945 Simplifying x = 0.8744917945Subproblem 2
x + 0.8333333335 = -1.707825128 Simplifying x + 0.8333333335 = -1.707825128 Reorder the terms: 0.8333333335 + x = -1.707825128 Solving 0.8333333335 + x = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.707825128 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.707825128 + -0.8333333335 x = -1.707825128 + -0.8333333335 Combine like terms: -1.707825128 + -0.8333333335 = -2.5411584615 x = -2.5411584615 Simplifying x = -2.5411584615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8744917945, -2.5411584615}
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