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Simplifying 4x2 + -32x = 5 Reorder the terms: -32x + 4x2 = 5 Solving -32x + 4x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -32x + 4x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -32x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -8x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -8x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -8x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -8x + x2 = 0 + 1.25 -8x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -8x + x2 = 1.25 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 = 1.25 + 16 Reorder the terms: 16 + -8x + x2 = 1.25 + 16 Combine like terms: 1.25 + 16 = 17.25 16 + -8x + x2 = 17.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + -4) equal to 4.153311931 and -4.153311931.Subproblem 1
x + -4 = 4.153311931 Simplifying x + -4 = 4.153311931 Reorder the terms: -4 + x = 4.153311931 Solving -4 + x = 4.153311931 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 = 4.153311931 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.153311931 + 4 x = 4.153311931 + 4 Combine like terms: 4.153311931 + 4 = 8.153311931 x = 8.153311931 Simplifying x = 8.153311931Subproblem 2
x + -4 = -4.153311931 Simplifying x + -4 = -4.153311931 Reorder the terms: -4 + x = -4.153311931 Solving -4 + x = -4.153311931 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 = -4.153311931 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.153311931 + 4 x = -4.153311931 + 4 Combine like terms: -4.153311931 + 4 = -0.153311931 x = -0.153311931 Simplifying x = -0.153311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.153311931, -0.153311931}
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