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Simplifying x(4x + 7) = 440 Reorder the terms: x(7 + 4x) = 440 (7 * x + 4x * x) = 440 (7x + 4x2) = 440 Solving 7x + 4x2 = 440 Solving for variable 'x'. Reorder the terms: -440 + 7x + 4x2 = 440 + -440 Combine like terms: 440 + -440 = 0 -440 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -110 + 1.75x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + 1.75x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 1.75x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 1.75x + x2 = 0 + 110 1.75x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 1.75x + x2 = 110 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 = 110 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 110 + 0.765625 Combine like terms: 110 + 0.765625 = 110.765625 0.765625 + 1.75x + x2 = 110.765625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 110.765625 Calculate the square root of the right side: 10.52452493 Break this problem into two subproblems by setting (x + 0.875) equal to 10.52452493 and -10.52452493.Subproblem 1
x + 0.875 = 10.52452493 Simplifying x + 0.875 = 10.52452493 Reorder the terms: 0.875 + x = 10.52452493 Solving 0.875 + x = 10.52452493 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 = 10.52452493 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 10.52452493 + -0.875 x = 10.52452493 + -0.875 Combine like terms: 10.52452493 + -0.875 = 9.64952493 x = 9.64952493 Simplifying x = 9.64952493Subproblem 2
x + 0.875 = -10.52452493 Simplifying x + 0.875 = -10.52452493 Reorder the terms: 0.875 + x = -10.52452493 Solving 0.875 + x = -10.52452493 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 = -10.52452493 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -10.52452493 + -0.875 x = -10.52452493 + -0.875 Combine like terms: -10.52452493 + -0.875 = -11.39952493 x = -11.39952493 Simplifying x = -11.39952493Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.64952493, -11.39952493}
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