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Simplifying 4x2 + -32x = 69 Reorder the terms: -32x + 4x2 = 69 Solving -32x + 4x2 = 69 Solving for variable 'x'. Reorder the terms: -69 + -32x + 4x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -69 + -32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.25 + -8x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + -8x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + -8x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + -8x + x2 = 0 + 17.25 -8x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 -8x + x2 = 17.25 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 17.25 + 16 Reorder the terms: 16 + -8x + x2 = 17.25 + 16 Combine like terms: 17.25 + 16 = 33.25 16 + -8x + x2 = 33.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + -4) equal to 5.766281297 and -5.766281297.Subproblem 1
x + -4 = 5.766281297 Simplifying x + -4 = 5.766281297 Reorder the terms: -4 + x = 5.766281297 Solving -4 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.766281297 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.766281297 + 4 x = 5.766281297 + 4 Combine like terms: 5.766281297 + 4 = 9.766281297 x = 9.766281297 Simplifying x = 9.766281297Subproblem 2
x + -4 = -5.766281297 Simplifying x + -4 = -5.766281297 Reorder the terms: -4 + x = -5.766281297 Solving -4 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.766281297 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.766281297 + 4 x = -5.766281297 + 4 Combine like terms: -5.766281297 + 4 = -1.766281297 x = -1.766281297 Simplifying x = -1.766281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.766281297, -1.766281297}
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