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Simplifying -4x2 + 24x + -29 = 0 Reorder the terms: -29 + 24x + -4x2 = 0 Solving -29 + 24x + -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'. 7.25 + -6x + x2 = 0 Move the constant term to the right: Add '-7.25' to each side of the equation. 7.25 + -6x + -7.25 + x2 = 0 + -7.25 Reorder the terms: 7.25 + -7.25 + -6x + x2 = 0 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + -6x + x2 = 0 + -7.25 -6x + x2 = 0 + -7.25 Combine like terms: 0 + -7.25 = -7.25 -6x + x2 = -7.25 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -7.25 + 9 Reorder the terms: 9 + -6x + x2 = -7.25 + 9 Combine like terms: -7.25 + 9 = 1.75 9 + -6x + x2 = 1.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -3) equal to 1.322875656 and -1.322875656.Subproblem 1
x + -3 = 1.322875656 Simplifying x + -3 = 1.322875656 Reorder the terms: -3 + x = 1.322875656 Solving -3 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.322875656 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.322875656 + 3 x = 1.322875656 + 3 Combine like terms: 1.322875656 + 3 = 4.322875656 x = 4.322875656 Simplifying x = 4.322875656Subproblem 2
x + -3 = -1.322875656 Simplifying x + -3 = -1.322875656 Reorder the terms: -3 + x = -1.322875656 Solving -3 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.322875656 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.322875656 + 3 x = -1.322875656 + 3 Combine like terms: -1.322875656 + 3 = 1.677124344 x = 1.677124344 Simplifying x = 1.677124344Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.322875656, 1.677124344}
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