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Simplifying 4x2 + 34x + -19 = 0 Reorder the terms: -19 + 34x + 4x2 = 0 Solving -19 + 34x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.75 + 8.5x + x2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + 8.5x + 4.75 + x2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + 8.5x + x2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + 8.5x + x2 = 0 + 4.75 8.5x + x2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 8.5x + x2 = 4.75 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 4.75 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 4.75 + 18.0625 Combine like terms: 4.75 + 18.0625 = 22.8125 18.0625 + 8.5x + x2 = 22.8125 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 22.8125 Calculate the square root of the right side: 4.776243294 Break this problem into two subproblems by setting (x + 4.25) equal to 4.776243294 and -4.776243294.Subproblem 1
x + 4.25 = 4.776243294 Simplifying x + 4.25 = 4.776243294 Reorder the terms: 4.25 + x = 4.776243294 Solving 4.25 + x = 4.776243294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 4.776243294 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 4.776243294 + -4.25 x = 4.776243294 + -4.25 Combine like terms: 4.776243294 + -4.25 = 0.526243294 x = 0.526243294 Simplifying x = 0.526243294Subproblem 2
x + 4.25 = -4.776243294 Simplifying x + 4.25 = -4.776243294 Reorder the terms: 4.25 + x = -4.776243294 Solving 4.25 + x = -4.776243294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -4.776243294 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -4.776243294 + -4.25 x = -4.776243294 + -4.25 Combine like terms: -4.776243294 + -4.25 = -9.026243294 x = -9.026243294 Simplifying x = -9.026243294Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.526243294, -9.026243294}
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