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Simplifying 3x + 8x(x + -1.9) = 7.9 Reorder the terms: 3x + 8x(-1.9 + x) = 7.9 3x + (-1.9 * 8x + x * 8x) = 7.9 3x + (-15.2x + 8x2) = 7.9 Combine like terms: 3x + -15.2x = -12.2x -12.2x + 8x2 = 7.9 Solving -12.2x + 8x2 = 7.9 Solving for variable 'x'. Reorder the terms: -7.9 + -12.2x + 8x2 = 7.9 + -7.9 Combine like terms: 7.9 + -7.9 = 0.0 -7.9 + -12.2x + 8x2 = 0.0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.9875 + -1.525x + x2 = 0.0 Move the constant term to the right: Add '0.9875' to each side of the equation. -0.9875 + -1.525x + 0.9875 + x2 = 0.0 + 0.9875 Reorder the terms: -0.9875 + 0.9875 + -1.525x + x2 = 0.0 + 0.9875 Combine like terms: -0.9875 + 0.9875 = 0.0000 0.0000 + -1.525x + x2 = 0.0 + 0.9875 -1.525x + x2 = 0.0 + 0.9875 Combine like terms: 0.0 + 0.9875 = 0.9875 -1.525x + x2 = 0.9875 The x term is -1.525x. Take half its coefficient (-0.7625). Square it (0.58140625) and add it to both sides. Add '0.58140625' to each side of the equation. -1.525x + 0.58140625 + x2 = 0.9875 + 0.58140625 Reorder the terms: 0.58140625 + -1.525x + x2 = 0.9875 + 0.58140625 Combine like terms: 0.9875 + 0.58140625 = 1.56890625 0.58140625 + -1.525x + x2 = 1.56890625 Factor a perfect square on the left side: (x + -0.7625)(x + -0.7625) = 1.56890625 Calculate the square root of the right side: 1.252559879 Break this problem into two subproblems by setting (x + -0.7625) equal to 1.252559879 and -1.252559879.Subproblem 1
x + -0.7625 = 1.252559879 Simplifying x + -0.7625 = 1.252559879 Reorder the terms: -0.7625 + x = 1.252559879 Solving -0.7625 + x = 1.252559879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7625' to each side of the equation. -0.7625 + 0.7625 + x = 1.252559879 + 0.7625 Combine like terms: -0.7625 + 0.7625 = 0.0000 0.0000 + x = 1.252559879 + 0.7625 x = 1.252559879 + 0.7625 Combine like terms: 1.252559879 + 0.7625 = 2.015059879 x = 2.015059879 Simplifying x = 2.015059879Subproblem 2
x + -0.7625 = -1.252559879 Simplifying x + -0.7625 = -1.252559879 Reorder the terms: -0.7625 + x = -1.252559879 Solving -0.7625 + x = -1.252559879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7625' to each side of the equation. -0.7625 + 0.7625 + x = -1.252559879 + 0.7625 Combine like terms: -0.7625 + 0.7625 = 0.0000 0.0000 + x = -1.252559879 + 0.7625 x = -1.252559879 + 0.7625 Combine like terms: -1.252559879 + 0.7625 = -0.490059879 x = -0.490059879 Simplifying x = -0.490059879Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.015059879, -0.490059879}
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