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Simplifying 2x2 + 3 + 5x + -1 + x2 = 4 + -1x2 + -2x + -3 Reorder the terms: 3 + -1 + 5x + 2x2 + x2 = 4 + -1x2 + -2x + -3 Combine like terms: 3 + -1 = 2 2 + 5x + 2x2 + x2 = 4 + -1x2 + -2x + -3 Combine like terms: 2x2 + x2 = 3x2 2 + 5x + 3x2 = 4 + -1x2 + -2x + -3 Reorder the terms: 2 + 5x + 3x2 = 4 + -3 + -2x + -1x2 Combine like terms: 4 + -3 = 1 2 + 5x + 3x2 = 1 + -2x + -1x2 Solving 2 + 5x + 3x2 = 1 + -2x + -1x2 Solving for variable 'x'. Reorder the terms: 2 + -1 + 5x + 2x + 3x2 + x2 = 1 + -2x + -1x2 + -1 + 2x + x2 Combine like terms: 2 + -1 = 1 1 + 5x + 2x + 3x2 + x2 = 1 + -2x + -1x2 + -1 + 2x + x2 Combine like terms: 5x + 2x = 7x 1 + 7x + 3x2 + x2 = 1 + -2x + -1x2 + -1 + 2x + x2 Combine like terms: 3x2 + x2 = 4x2 1 + 7x + 4x2 = 1 + -2x + -1x2 + -1 + 2x + x2 Reorder the terms: 1 + 7x + 4x2 = 1 + -1 + -2x + 2x + -1x2 + x2 Combine like terms: 1 + -1 = 0 1 + 7x + 4x2 = 0 + -2x + 2x + -1x2 + x2 1 + 7x + 4x2 = -2x + 2x + -1x2 + x2 Combine like terms: -2x + 2x = 0 1 + 7x + 4x2 = 0 + -1x2 + x2 1 + 7x + 4x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.75x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.75x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.75x + x2 = 0 + -0.25 1.75x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.75x + x2 = -0.25 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 = -0.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -0.25 + 0.765625 Combine like terms: -0.25 + 0.765625 = 0.515625 0.765625 + 1.75x + x2 = 0.515625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (x + 0.875) equal to 0.718070331 and -0.718070331.Subproblem 1
x + 0.875 = 0.718070331 Simplifying x + 0.875 = 0.718070331 Reorder the terms: 0.875 + x = 0.718070331 Solving 0.875 + x = 0.718070331 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 = 0.718070331 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 0.718070331 + -0.875 x = 0.718070331 + -0.875 Combine like terms: 0.718070331 + -0.875 = -0.156929669 x = -0.156929669 Simplifying x = -0.156929669Subproblem 2
x + 0.875 = -0.718070331 Simplifying x + 0.875 = -0.718070331 Reorder the terms: 0.875 + x = -0.718070331 Solving 0.875 + x = -0.718070331 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 = -0.718070331 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -0.718070331 + -0.875 x = -0.718070331 + -0.875 Combine like terms: -0.718070331 + -0.875 = -1.593070331 x = -1.593070331 Simplifying x = -1.593070331Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.156929669, -1.593070331}
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