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Simplifying x(2x + 6) = 228 Reorder the terms: x(6 + 2x) = 228 (6 * x + 2x * x) = 228 (6x + 2x2) = 228 Solving 6x + 2x2 = 228 Solving for variable 'x'. Reorder the terms: -228 + 6x + 2x2 = 228 + -228 Combine like terms: 228 + -228 = 0 -228 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-114 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-114 + 3x + x2)' equal to zero and attempt to solve: Simplifying -114 + 3x + x2 = 0 Solving -114 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '114' to each side of the equation. -114 + 3x + 114 + x2 = 0 + 114 Reorder the terms: -114 + 114 + 3x + x2 = 0 + 114 Combine like terms: -114 + 114 = 0 0 + 3x + x2 = 0 + 114 3x + x2 = 0 + 114 Combine like terms: 0 + 114 = 114 3x + x2 = 114 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 114 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 114 + 2.25 Combine like terms: 114 + 2.25 = 116.25 2.25 + 3x + x2 = 116.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (x + 1.5) equal to 10.781929326 and -10.781929326.Subproblem 1
x + 1.5 = 10.781929326 Simplifying x + 1.5 = 10.781929326 Reorder the terms: 1.5 + x = 10.781929326 Solving 1.5 + x = 10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.781929326 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.781929326 + -1.5 x = 10.781929326 + -1.5 Combine like terms: 10.781929326 + -1.5 = 9.281929326 x = 9.281929326 Simplifying x = 9.281929326Subproblem 2
x + 1.5 = -10.781929326 Simplifying x + 1.5 = -10.781929326 Reorder the terms: 1.5 + x = -10.781929326 Solving 1.5 + x = -10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.781929326 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.781929326 + -1.5 x = -10.781929326 + -1.5 Combine like terms: -10.781929326 + -1.5 = -12.281929326 x = -12.281929326 Simplifying x = -12.281929326Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.281929326, -12.281929326}Solution
x = {9.281929326, -12.281929326}
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