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Simplifying 3x(5x + -1) + -1(2x + -3) = -1(-7 + -1x) Reorder the terms: 3x(-1 + 5x) + -1(2x + -3) = -1(-7 + -1x) (-1 * 3x + 5x * 3x) + -1(2x + -3) = -1(-7 + -1x) (-3x + 15x2) + -1(2x + -3) = -1(-7 + -1x) Reorder the terms: -3x + 15x2 + -1(-3 + 2x) = -1(-7 + -1x) -3x + 15x2 + (-3 * -1 + 2x * -1) = -1(-7 + -1x) -3x + 15x2 + (3 + -2x) = -1(-7 + -1x) Reorder the terms: 3 + -3x + -2x + 15x2 = -1(-7 + -1x) Combine like terms: -3x + -2x = -5x 3 + -5x + 15x2 = -1(-7 + -1x) 3 + -5x + 15x2 = (-7 * -1 + -1x * -1) 3 + -5x + 15x2 = (7 + 1x) Solving 3 + -5x + 15x2 = 7 + 1x Solving for variable 'x'. Reorder the terms: 3 + -7 + -5x + -1x + 15x2 = 7 + 1x + -7 + -1x Combine like terms: 3 + -7 = -4 -4 + -5x + -1x + 15x2 = 7 + 1x + -7 + -1x Combine like terms: -5x + -1x = -6x -4 + -6x + 15x2 = 7 + 1x + -7 + -1x Reorder the terms: -4 + -6x + 15x2 = 7 + -7 + 1x + -1x Combine like terms: 7 + -7 = 0 -4 + -6x + 15x2 = 0 + 1x + -1x -4 + -6x + 15x2 = 1x + -1x Combine like terms: 1x + -1x = 0 -4 + -6x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.2666666667 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.2666666667' to each side of the equation. -0.2666666667 + -0.4x + 0.2666666667 + x2 = 0 + 0.2666666667 Reorder the terms: -0.2666666667 + 0.2666666667 + -0.4x + x2 = 0 + 0.2666666667 Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000 0.0000000000 + -0.4x + x2 = 0 + 0.2666666667 -0.4x + x2 = 0 + 0.2666666667 Combine like terms: 0 + 0.2666666667 = 0.2666666667 -0.4x + x2 = 0.2666666667 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.2666666667 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.2666666667 + 0.04 Combine like terms: 0.2666666667 + 0.04 = 0.3066666667 0.04 + -0.4x + x2 = 0.3066666667 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.3066666667 Calculate the square root of the right side: 0.553774924 Break this problem into two subproblems by setting (x + -0.2) equal to 0.553774924 and -0.553774924.Subproblem 1
x + -0.2 = 0.553774924 Simplifying x + -0.2 = 0.553774924 Reorder the terms: -0.2 + x = 0.553774924 Solving -0.2 + x = 0.553774924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.553774924 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.553774924 + 0.2 x = 0.553774924 + 0.2 Combine like terms: 0.553774924 + 0.2 = 0.753774924 x = 0.753774924 Simplifying x = 0.753774924Subproblem 2
x + -0.2 = -0.553774924 Simplifying x + -0.2 = -0.553774924 Reorder the terms: -0.2 + x = -0.553774924 Solving -0.2 + x = -0.553774924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.553774924 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.553774924 + 0.2 x = -0.553774924 + 0.2 Combine like terms: -0.553774924 + 0.2 = -0.353774924 x = -0.353774924 Simplifying x = -0.353774924Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.753774924, -0.353774924}
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