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Simplifying 8(x + -2) * 7x + 1 = -18 Reorder the terms: 8(-2 + x) * 7x + 1 = -18 Reorder the terms for easier multiplication: 8 * 7x(-2 + x) + 1 = -18 Multiply 8 * 7 56x(-2 + x) + 1 = -18 (-2 * 56x + x * 56x) + 1 = -18 (-112x + 56x2) + 1 = -18 Reorder the terms: 1 + -112x + 56x2 = -18 Solving 1 + -112x + 56x2 = -18 Solving for variable 'x'. Reorder the terms: 1 + 18 + -112x + 56x2 = -18 + 18 Combine like terms: 1 + 18 = 19 19 + -112x + 56x2 = -18 + 18 Combine like terms: -18 + 18 = 0 19 + -112x + 56x2 = 0 Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. 0.3392857143 + -2x + x2 = 0 Move the constant term to the right: Add '-0.3392857143' to each side of the equation. 0.3392857143 + -2x + -0.3392857143 + x2 = 0 + -0.3392857143 Reorder the terms: 0.3392857143 + -0.3392857143 + -2x + x2 = 0 + -0.3392857143 Combine like terms: 0.3392857143 + -0.3392857143 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.3392857143 -2x + x2 = 0 + -0.3392857143 Combine like terms: 0 + -0.3392857143 = -0.3392857143 -2x + x2 = -0.3392857143 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.3392857143 + 1 Reorder the terms: 1 + -2x + x2 = -0.3392857143 + 1 Combine like terms: -0.3392857143 + 1 = 0.6607142857 1 + -2x + x2 = 0.6607142857 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.6607142857 Calculate the square root of the right side: 0.812843334 Break this problem into two subproblems by setting (x + -1) equal to 0.812843334 and -0.812843334.Subproblem 1
x + -1 = 0.812843334 Simplifying x + -1 = 0.812843334 Reorder the terms: -1 + x = 0.812843334 Solving -1 + x = 0.812843334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.812843334 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.812843334 + 1 x = 0.812843334 + 1 Combine like terms: 0.812843334 + 1 = 1.812843334 x = 1.812843334 Simplifying x = 1.812843334Subproblem 2
x + -1 = -0.812843334 Simplifying x + -1 = -0.812843334 Reorder the terms: -1 + x = -0.812843334 Solving -1 + x = -0.812843334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.812843334 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.812843334 + 1 x = -0.812843334 + 1 Combine like terms: -0.812843334 + 1 = 0.187156666 x = 0.187156666 Simplifying x = 0.187156666Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.812843334, 0.187156666}
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