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Simplifying 5x(2x + -3) + -2x(x + -1) + -8x + 7x + -3 = 0 Reorder the terms: 5x(-3 + 2x) + -2x(x + -1) + -8x + 7x + -3 = 0 (-3 * 5x + 2x * 5x) + -2x(x + -1) + -8x + 7x + -3 = 0 (-15x + 10x2) + -2x(x + -1) + -8x + 7x + -3 = 0 Reorder the terms: -15x + 10x2 + -2x(-1 + x) + -8x + 7x + -3 = 0 -15x + 10x2 + (-1 * -2x + x * -2x) + -8x + 7x + -3 = 0 -15x + 10x2 + (2x + -2x2) + -8x + 7x + -3 = 0 Reorder the terms: -3 + -15x + 2x + -8x + 7x + 10x2 + -2x2 = 0 Combine like terms: -15x + 2x = -13x -3 + -13x + -8x + 7x + 10x2 + -2x2 = 0 Combine like terms: -13x + -8x = -21x -3 + -21x + 7x + 10x2 + -2x2 = 0 Combine like terms: -21x + 7x = -14x -3 + -14x + 10x2 + -2x2 = 0 Combine like terms: 10x2 + -2x2 = 8x2 -3 + -14x + 8x2 = 0 Solving -3 + -14x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -1.75x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -1.75x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -1.75x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -1.75x + x2 = 0 + 0.375 -1.75x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -1.75x + x2 = 0.375 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 = 0.375 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 0.375 + 0.765625 Combine like terms: 0.375 + 0.765625 = 1.140625 0.765625 + -1.75x + x2 = 1.140625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + -0.875) equal to 1.068000468 and -1.068000468.Subproblem 1
x + -0.875 = 1.068000468 Simplifying x + -0.875 = 1.068000468 Reorder the terms: -0.875 + x = 1.068000468 Solving -0.875 + x = 1.068000468 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 = 1.068000468 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.068000468 + 0.875 x = 1.068000468 + 0.875 Combine like terms: 1.068000468 + 0.875 = 1.943000468 x = 1.943000468 Simplifying x = 1.943000468Subproblem 2
x + -0.875 = -1.068000468 Simplifying x + -0.875 = -1.068000468 Reorder the terms: -0.875 + x = -1.068000468 Solving -0.875 + x = -1.068000468 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 = -1.068000468 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.068000468 + 0.875 x = -1.068000468 + 0.875 Combine like terms: -1.068000468 + 0.875 = -0.193000468 x = -0.193000468 Simplifying x = -0.193000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.943000468, -0.193000468}
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