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Simplifying 204 = 4x2 + 6x Reorder the terms: 204 = 6x + 4x2 Solving 204 = 6x + 4x2 Solving for variable 'x'. Reorder the terms: 204 + -6x + -4x2 = 6x + -6x + 4x2 + -4x2 Combine like terms: 6x + -6x = 0 204 + -6x + -4x2 = 0 + 4x2 + -4x2 204 + -6x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 204 + -6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(102 + -3x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(102 + -3x + -2x2)' equal to zero and attempt to solve: Simplifying 102 + -3x + -2x2 = 0 Solving 102 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -51 + 1.5x + x2 = 0 Move the constant term to the right: Add '51' to each side of the equation. -51 + 1.5x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 1.5x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 1.5x + x2 = 0 + 51 1.5x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 1.5x + x2 = 51 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 51 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 51 + 0.5625 Combine like terms: 51 + 0.5625 = 51.5625 0.5625 + 1.5x + x2 = 51.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 51.5625 Calculate the square root of the right side: 7.180703308 Break this problem into two subproblems by setting (x + 0.75) equal to 7.180703308 and -7.180703308.Subproblem 1
x + 0.75 = 7.180703308 Simplifying x + 0.75 = 7.180703308 Reorder the terms: 0.75 + x = 7.180703308 Solving 0.75 + x = 7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 7.180703308 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 7.180703308 + -0.75 x = 7.180703308 + -0.75 Combine like terms: 7.180703308 + -0.75 = 6.430703308 x = 6.430703308 Simplifying x = 6.430703308Subproblem 2
x + 0.75 = -7.180703308 Simplifying x + 0.75 = -7.180703308 Reorder the terms: 0.75 + x = -7.180703308 Solving 0.75 + x = -7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -7.180703308 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -7.180703308 + -0.75 x = -7.180703308 + -0.75 Combine like terms: -7.180703308 + -0.75 = -7.930703308 x = -7.930703308 Simplifying x = -7.930703308Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.430703308, -7.930703308}Solution
x = {6.430703308, -7.930703308}
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