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Simplifying 7x + -3 = 4x(2x + -3) Reorder the terms: -3 + 7x = 4x(2x + -3) Reorder the terms: -3 + 7x = 4x(-3 + 2x) -3 + 7x = (-3 * 4x + 2x * 4x) -3 + 7x = (-12x + 8x2) Solving -3 + 7x = -12x + 8x2 Solving for variable 'x'. Combine like terms: 7x + 12x = 19x -3 + 19x + -8x2 = -12x + 8x2 + 12x + -8x2 Reorder the terms: -3 + 19x + -8x2 = -12x + 12x + 8x2 + -8x2 Combine like terms: -12x + 12x = 0 -3 + 19x + -8x2 = 0 + 8x2 + -8x2 -3 + 19x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -3 + 19x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.375 + -2.375x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -2.375x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -2.375x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -2.375x + x2 = 0 + -0.375 -2.375x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -2.375x + x2 = -0.375 The x term is -2.375x. Take half its coefficient (-1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. -2.375x + 1.41015625 + x2 = -0.375 + 1.41015625 Reorder the terms: 1.41015625 + -2.375x + x2 = -0.375 + 1.41015625 Combine like terms: -0.375 + 1.41015625 = 1.03515625 1.41015625 + -2.375x + x2 = 1.03515625 Factor a perfect square on the left side: (x + -1.1875)(x + -1.1875) = 1.03515625 Calculate the square root of the right side: 1.017426287 Break this problem into two subproblems by setting (x + -1.1875) equal to 1.017426287 and -1.017426287.Subproblem 1
x + -1.1875 = 1.017426287 Simplifying x + -1.1875 = 1.017426287 Reorder the terms: -1.1875 + x = 1.017426287 Solving -1.1875 + x = 1.017426287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = 1.017426287 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = 1.017426287 + 1.1875 x = 1.017426287 + 1.1875 Combine like terms: 1.017426287 + 1.1875 = 2.204926287 x = 2.204926287 Simplifying x = 2.204926287Subproblem 2
x + -1.1875 = -1.017426287 Simplifying x + -1.1875 = -1.017426287 Reorder the terms: -1.1875 + x = -1.017426287 Solving -1.1875 + x = -1.017426287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = -1.017426287 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = -1.017426287 + 1.1875 x = -1.017426287 + 1.1875 Combine like terms: -1.017426287 + 1.1875 = 0.170073713 x = 0.170073713 Simplifying x = 0.170073713Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.204926287, 0.170073713}
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