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Simplifying 5 + -3x2 = 7x + x2 Solving 5 + -3x2 = 7x + x2 Solving for variable 'x'. Reorder the terms: 5 + -7x + -3x2 + -1x2 = 7x + x2 + -7x + -1x2 Combine like terms: -3x2 + -1x2 = -4x2 5 + -7x + -4x2 = 7x + x2 + -7x + -1x2 Reorder the terms: 5 + -7x + -4x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 5 + -7x + -4x2 = 0 + x2 + -1x2 5 + -7x + -4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + -7x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.75x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.75x + x2 = 0 + 1.25 1.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.75x + x2 = 1.25 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 1.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 1.25 + 0.765625 Combine like terms: 1.25 + 0.765625 = 2.015625 0.765625 + 1.75x + x2 = 2.015625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (x + 0.875) equal to 1.419727086 and -1.419727086.Subproblem 1
x + 0.875 = 1.419727086 Simplifying x + 0.875 = 1.419727086 Reorder the terms: 0.875 + x = 1.419727086 Solving 0.875 + x = 1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.419727086 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.419727086 + -0.875 x = 1.419727086 + -0.875 Combine like terms: 1.419727086 + -0.875 = 0.544727086 x = 0.544727086 Simplifying x = 0.544727086Subproblem 2
x + 0.875 = -1.419727086 Simplifying x + 0.875 = -1.419727086 Reorder the terms: 0.875 + x = -1.419727086 Solving 0.875 + x = -1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.419727086 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.419727086 + -0.875 x = -1.419727086 + -0.875 Combine like terms: -1.419727086 + -0.875 = -2.294727086 x = -2.294727086 Simplifying x = -2.294727086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.544727086, -2.294727086}
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