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Simplifying -16x2 + -19x + 234 = 0 Reorder the terms: 234 + -19x + -16x2 = 0 Solving 234 + -19x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -14.625 + 1.1875x + x2 = 0 Move the constant term to the right: Add '14.625' to each side of the equation. -14.625 + 1.1875x + 14.625 + x2 = 0 + 14.625 Reorder the terms: -14.625 + 14.625 + 1.1875x + x2 = 0 + 14.625 Combine like terms: -14.625 + 14.625 = 0.000 0.000 + 1.1875x + x2 = 0 + 14.625 1.1875x + x2 = 0 + 14.625 Combine like terms: 0 + 14.625 = 14.625 1.1875x + x2 = 14.625 The x term is 1.1875x. Take half its coefficient (0.59375). Square it (0.3525390625) and add it to both sides. Add '0.3525390625' to each side of the equation. 1.1875x + 0.3525390625 + x2 = 14.625 + 0.3525390625 Reorder the terms: 0.3525390625 + 1.1875x + x2 = 14.625 + 0.3525390625 Combine like terms: 14.625 + 0.3525390625 = 14.9775390625 0.3525390625 + 1.1875x + x2 = 14.9775390625 Factor a perfect square on the left side: (x + 0.59375)(x + 0.59375) = 14.9775390625 Calculate the square root of the right side: 3.870082565 Break this problem into two subproblems by setting (x + 0.59375) equal to 3.870082565 and -3.870082565.Subproblem 1
x + 0.59375 = 3.870082565 Simplifying x + 0.59375 = 3.870082565 Reorder the terms: 0.59375 + x = 3.870082565 Solving 0.59375 + x = 3.870082565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + x = 3.870082565 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + x = 3.870082565 + -0.59375 x = 3.870082565 + -0.59375 Combine like terms: 3.870082565 + -0.59375 = 3.276332565 x = 3.276332565 Simplifying x = 3.276332565Subproblem 2
x + 0.59375 = -3.870082565 Simplifying x + 0.59375 = -3.870082565 Reorder the terms: 0.59375 + x = -3.870082565 Solving 0.59375 + x = -3.870082565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.59375' to each side of the equation. 0.59375 + -0.59375 + x = -3.870082565 + -0.59375 Combine like terms: 0.59375 + -0.59375 = 0.00000 0.00000 + x = -3.870082565 + -0.59375 x = -3.870082565 + -0.59375 Combine like terms: -3.870082565 + -0.59375 = -4.463832565 x = -4.463832565 Simplifying x = -4.463832565Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.276332565, -4.463832565}
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