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Simplifying -16x2 + 62x + 23 = 0 Reorder the terms: 23 + 62x + -16x2 = 0 Solving 23 + 62x + -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'. -1.4375 + -3.875x + x2 = 0 Move the constant term to the right: Add '1.4375' to each side of the equation. -1.4375 + -3.875x + 1.4375 + x2 = 0 + 1.4375 Reorder the terms: -1.4375 + 1.4375 + -3.875x + x2 = 0 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + -3.875x + x2 = 0 + 1.4375 -3.875x + x2 = 0 + 1.4375 Combine like terms: 0 + 1.4375 = 1.4375 -3.875x + x2 = 1.4375 The x term is -3.875x. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875x + 3.75390625 + x2 = 1.4375 + 3.75390625 Reorder the terms: 3.75390625 + -3.875x + x2 = 1.4375 + 3.75390625 Combine like terms: 1.4375 + 3.75390625 = 5.19140625 3.75390625 + -3.875x + x2 = 5.19140625 Factor a perfect square on the left side: (x + -1.9375)(x + -1.9375) = 5.19140625 Calculate the square root of the right side: 2.278465767 Break this problem into two subproblems by setting (x + -1.9375) equal to 2.278465767 and -2.278465767.Subproblem 1
x + -1.9375 = 2.278465767 Simplifying x + -1.9375 = 2.278465767 Reorder the terms: -1.9375 + x = 2.278465767 Solving -1.9375 + x = 2.278465767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = 2.278465767 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = 2.278465767 + 1.9375 x = 2.278465767 + 1.9375 Combine like terms: 2.278465767 + 1.9375 = 4.215965767 x = 4.215965767 Simplifying x = 4.215965767Subproblem 2
x + -1.9375 = -2.278465767 Simplifying x + -1.9375 = -2.278465767 Reorder the terms: -1.9375 + x = -2.278465767 Solving -1.9375 + x = -2.278465767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + x = -2.278465767 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + x = -2.278465767 + 1.9375 x = -2.278465767 + 1.9375 Combine like terms: -2.278465767 + 1.9375 = -0.340965767 x = -0.340965767 Simplifying x = -0.340965767Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.215965767, -0.340965767}
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