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Simplifying 2x(88 + 3x) + 4 + -4x = 0 (88 * 2x + 3x * 2x) + 4 + -4x = 0 (176x + 6x2) + 4 + -4x = 0 Reorder the terms: 4 + 176x + -4x + 6x2 = 0 Combine like terms: 176x + -4x = 172x 4 + 172x + 6x2 = 0 Solving 4 + 172x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 86x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 86x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + 86x + 3x2 = 0 Solving 2 + 86x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 28.66666667x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 28.66666667x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 28.66666667x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 28.66666667x + x2 = 0 + -0.6666666667 28.66666667x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 28.66666667x + x2 = -0.6666666667 The x term is 28.66666667x. Take half its coefficient (14.33333334). Square it (205.4444446) and add it to both sides. Add '205.4444446' to each side of the equation. 28.66666667x + 205.4444446 + x2 = -0.6666666667 + 205.4444446 Reorder the terms: 205.4444446 + 28.66666667x + x2 = -0.6666666667 + 205.4444446 Combine like terms: -0.6666666667 + 205.4444446 = 204.7777779333 205.4444446 + 28.66666667x + x2 = 204.7777779333 Factor a perfect square on the left side: (x + 14.33333334)(x + 14.33333334) = 204.7777779333 Calculate the square root of the right side: 14.310058628 Break this problem into two subproblems by setting (x + 14.33333334) equal to 14.310058628 and -14.310058628.Subproblem 1
x + 14.33333334 = 14.310058628 Simplifying x + 14.33333334 = 14.310058628 Reorder the terms: 14.33333334 + x = 14.310058628 Solving 14.33333334 + x = 14.310058628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.33333334' to each side of the equation. 14.33333334 + -14.33333334 + x = 14.310058628 + -14.33333334 Combine like terms: 14.33333334 + -14.33333334 = 0.00000000 0.00000000 + x = 14.310058628 + -14.33333334 x = 14.310058628 + -14.33333334 Combine like terms: 14.310058628 + -14.33333334 = -0.023274712 x = -0.023274712 Simplifying x = -0.023274712Subproblem 2
x + 14.33333334 = -14.310058628 Simplifying x + 14.33333334 = -14.310058628 Reorder the terms: 14.33333334 + x = -14.310058628 Solving 14.33333334 + x = -14.310058628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.33333334' to each side of the equation. 14.33333334 + -14.33333334 + x = -14.310058628 + -14.33333334 Combine like terms: 14.33333334 + -14.33333334 = 0.00000000 0.00000000 + x = -14.310058628 + -14.33333334 x = -14.310058628 + -14.33333334 Combine like terms: -14.310058628 + -14.33333334 = -28.643391968 x = -28.643391968 Simplifying x = -28.643391968Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.023274712, -28.643391968}Solution
x = {-0.023274712, -28.643391968}
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