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Simplifying 6x + 16x2 = 36 Solving 6x + 16x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + 6x + 16x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 6x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 3x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 3x + 8x2)' equal to zero and attempt to solve: Simplifying -18 + 3x + 8x2 = 0 Solving -18 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.25 + 0.375x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 0.375x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 0.375x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 0.375x + x2 = 0 + 2.25 0.375x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 0.375x + x2 = 2.25 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 2.25 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 2.25 + 0.03515625 Combine like terms: 2.25 + 0.03515625 = 2.28515625 0.03515625 + 0.375x + x2 = 2.28515625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 2.28515625 Calculate the square root of the right side: 1.511673328 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.511673328 and -1.511673328.Subproblem 1
x + 0.1875 = 1.511673328 Simplifying x + 0.1875 = 1.511673328 Reorder the terms: 0.1875 + x = 1.511673328 Solving 0.1875 + x = 1.511673328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.511673328 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.511673328 + -0.1875 x = 1.511673328 + -0.1875 Combine like terms: 1.511673328 + -0.1875 = 1.324173328 x = 1.324173328 Simplifying x = 1.324173328Subproblem 2
x + 0.1875 = -1.511673328 Simplifying x + 0.1875 = -1.511673328 Reorder the terms: 0.1875 + x = -1.511673328 Solving 0.1875 + x = -1.511673328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.511673328 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.511673328 + -0.1875 x = -1.511673328 + -0.1875 Combine like terms: -1.511673328 + -0.1875 = -1.699173328 x = -1.699173328 Simplifying x = -1.699173328Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.324173328, -1.699173328}Solution
x = {1.324173328, -1.699173328}
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