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Simplifying 5x(7x + 4)(7 + 4) = 158 Reorder the terms: 5x(4 + 7x)(7 + 4) = 158 Combine like terms: 7 + 4 = 11 5x(4 + 7x)(11) = 158 Reorder the terms for easier multiplication: 5 * 11x(4 + 7x) = 158 Multiply 5 * 11 55x(4 + 7x) = 158 (4 * 55x + 7x * 55x) = 158 (220x + 385x2) = 158 Solving 220x + 385x2 = 158 Solving for variable 'x'. Reorder the terms: -158 + 220x + 385x2 = 158 + -158 Combine like terms: 158 + -158 = 0 -158 + 220x + 385x2 = 0 Begin completing the square. Divide all terms by 385 the coefficient of the squared term: Divide each side by '385'. -0.4103896104 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.4103896104' to each side of the equation. -0.4103896104 + 0.5714285714x + 0.4103896104 + x2 = 0 + 0.4103896104 Reorder the terms: -0.4103896104 + 0.4103896104 + 0.5714285714x + x2 = 0 + 0.4103896104 Combine like terms: -0.4103896104 + 0.4103896104 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + 0.4103896104 0.5714285714x + x2 = 0 + 0.4103896104 Combine like terms: 0 + 0.4103896104 = 0.4103896104 0.5714285714x + x2 = 0.4103896104 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 0.4103896104 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.4103896104 + 0.08163265305 Combine like terms: 0.4103896104 + 0.08163265305 = 0.49202226345 0.08163265305 + 0.5714285714x + x2 = 0.49202226345 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.49202226345 Calculate the square root of the right side: 0.701442987 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.701442987 and -0.701442987.Subproblem 1
x + 0.2857142857 = 0.701442987 Simplifying x + 0.2857142857 = 0.701442987 Reorder the terms: 0.2857142857 + x = 0.701442987 Solving 0.2857142857 + x = 0.701442987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 0.701442987 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.701442987 + -0.2857142857 x = 0.701442987 + -0.2857142857 Combine like terms: 0.701442987 + -0.2857142857 = 0.4157287013 x = 0.4157287013 Simplifying x = 0.4157287013Subproblem 2
x + 0.2857142857 = -0.701442987 Simplifying x + 0.2857142857 = -0.701442987 Reorder the terms: 0.2857142857 + x = -0.701442987 Solving 0.2857142857 + x = -0.701442987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -0.701442987 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.701442987 + -0.2857142857 x = -0.701442987 + -0.2857142857 Combine like terms: -0.701442987 + -0.2857142857 = -0.9871572727 x = -0.9871572727 Simplifying x = -0.9871572727Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4157287013, -0.9871572727}
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