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Simplifying 0 = 4x2 + 7x + -132 Reorder the terms: 0 = -132 + 7x + 4x2 Solving 0 = -132 + 7x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 132 = 132 132 + -7x + -4x2 = -132 + 7x + 4x2 + 132 + -7x + -4x2 Reorder the terms: 132 + -7x + -4x2 = -132 + 132 + 7x + -7x + 4x2 + -4x2 Combine like terms: -132 + 132 = 0 132 + -7x + -4x2 = 0 + 7x + -7x + 4x2 + -4x2 132 + -7x + -4x2 = 7x + -7x + 4x2 + -4x2 Combine like terms: 7x + -7x = 0 132 + -7x + -4x2 = 0 + 4x2 + -4x2 132 + -7x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 132 + -7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -33 + 1.75x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 1.75x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 1.75x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 1.75x + x2 = 0 + 33 1.75x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 1.75x + x2 = 33 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 33 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 33 + 0.765625 Combine like terms: 33 + 0.765625 = 33.765625 0.765625 + 1.75x + x2 = 33.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 33.765625 Calculate the square root of the right side: 5.81081965 Break this problem into two subproblems by setting (x + 0.875) equal to 5.81081965 and -5.81081965.Subproblem 1
x + 0.875 = 5.81081965 Simplifying x + 0.875 = 5.81081965 Reorder the terms: 0.875 + x = 5.81081965 Solving 0.875 + x = 5.81081965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 5.81081965 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 5.81081965 + -0.875 x = 5.81081965 + -0.875 Combine like terms: 5.81081965 + -0.875 = 4.93581965 x = 4.93581965 Simplifying x = 4.93581965Subproblem 2
x + 0.875 = -5.81081965 Simplifying x + 0.875 = -5.81081965 Reorder the terms: 0.875 + x = -5.81081965 Solving 0.875 + x = -5.81081965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -5.81081965 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -5.81081965 + -0.875 x = -5.81081965 + -0.875 Combine like terms: -5.81081965 + -0.875 = -6.68581965 x = -6.68581965 Simplifying x = -6.68581965Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.93581965, -6.68581965}
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