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Simplifying 4x2 + 57x + 189 = 368 Reorder the terms: 189 + 57x + 4x2 = 368 Solving 189 + 57x + 4x2 = 368 Solving for variable 'x'. Reorder the terms: 189 + -368 + 57x + 4x2 = 368 + -368 Combine like terms: 189 + -368 = -179 -179 + 57x + 4x2 = 368 + -368 Combine like terms: 368 + -368 = 0 -179 + 57x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -44.75 + 14.25x + x2 = 0 Move the constant term to the right: Add '44.75' to each side of the equation. -44.75 + 14.25x + 44.75 + x2 = 0 + 44.75 Reorder the terms: -44.75 + 44.75 + 14.25x + x2 = 0 + 44.75 Combine like terms: -44.75 + 44.75 = 0.00 0.00 + 14.25x + x2 = 0 + 44.75 14.25x + x2 = 0 + 44.75 Combine like terms: 0 + 44.75 = 44.75 14.25x + x2 = 44.75 The x term is 14.25x. Take half its coefficient (7.125). Square it (50.765625) and add it to both sides. Add '50.765625' to each side of the equation. 14.25x + 50.765625 + x2 = 44.75 + 50.765625 Reorder the terms: 50.765625 + 14.25x + x2 = 44.75 + 50.765625 Combine like terms: 44.75 + 50.765625 = 95.515625 50.765625 + 14.25x + x2 = 95.515625 Factor a perfect square on the left side: (x + 7.125)(x + 7.125) = 95.515625 Calculate the square root of the right side: 9.773209555 Break this problem into two subproblems by setting (x + 7.125) equal to 9.773209555 and -9.773209555.Subproblem 1
x + 7.125 = 9.773209555 Simplifying x + 7.125 = 9.773209555 Reorder the terms: 7.125 + x = 9.773209555 Solving 7.125 + x = 9.773209555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.125' to each side of the equation. 7.125 + -7.125 + x = 9.773209555 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + x = 9.773209555 + -7.125 x = 9.773209555 + -7.125 Combine like terms: 9.773209555 + -7.125 = 2.648209555 x = 2.648209555 Simplifying x = 2.648209555Subproblem 2
x + 7.125 = -9.773209555 Simplifying x + 7.125 = -9.773209555 Reorder the terms: 7.125 + x = -9.773209555 Solving 7.125 + x = -9.773209555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.125' to each side of the equation. 7.125 + -7.125 + x = -9.773209555 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + x = -9.773209555 + -7.125 x = -9.773209555 + -7.125 Combine like terms: -9.773209555 + -7.125 = -16.898209555 x = -16.898209555 Simplifying x = -16.898209555Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.648209555, -16.898209555}
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