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Simplifying 3(x + -8) * 5x + 7 = 0 Reorder the terms: 3(-8 + x) * 5x + 7 = 0 Reorder the terms for easier multiplication: 3 * 5x(-8 + x) + 7 = 0 Multiply 3 * 5 15x(-8 + x) + 7 = 0 (-8 * 15x + x * 15x) + 7 = 0 (-120x + 15x2) + 7 = 0 Reorder the terms: 7 + -120x + 15x2 = 0 Solving 7 + -120x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.4666666667 + -8x + x2 = 0 Move the constant term to the right: Add '-0.4666666667' to each side of the equation. 0.4666666667 + -8x + -0.4666666667 + x2 = 0 + -0.4666666667 Reorder the terms: 0.4666666667 + -0.4666666667 + -8x + x2 = 0 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + -8x + x2 = 0 + -0.4666666667 -8x + x2 = 0 + -0.4666666667 Combine like terms: 0 + -0.4666666667 = -0.4666666667 -8x + x2 = -0.4666666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -0.4666666667 + 16 Reorder the terms: 16 + -8x + x2 = -0.4666666667 + 16 Combine like terms: -0.4666666667 + 16 = 15.5333333333 16 + -8x + x2 = 15.5333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.5333333333 Calculate the square root of the right side: 3.941235001 Break this problem into two subproblems by setting (x + -4) equal to 3.941235001 and -3.941235001.Subproblem 1
x + -4 = 3.941235001 Simplifying x + -4 = 3.941235001 Reorder the terms: -4 + x = 3.941235001 Solving -4 + x = 3.941235001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.941235001 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.941235001 + 4 x = 3.941235001 + 4 Combine like terms: 3.941235001 + 4 = 7.941235001 x = 7.941235001 Simplifying x = 7.941235001Subproblem 2
x + -4 = -3.941235001 Simplifying x + -4 = -3.941235001 Reorder the terms: -4 + x = -3.941235001 Solving -4 + x = -3.941235001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.941235001 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.941235001 + 4 x = -3.941235001 + 4 Combine like terms: -3.941235001 + 4 = 0.058764999 x = 0.058764999 Simplifying x = 0.058764999Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.941235001, 0.058764999}
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