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Simplifying 5x(x + -1) + -1(6x + 5) = 5(3x + 6) Reorder the terms: 5x(-1 + x) + -1(6x + 5) = 5(3x + 6) (-1 * 5x + x * 5x) + -1(6x + 5) = 5(3x + 6) (-5x + 5x2) + -1(6x + 5) = 5(3x + 6) Reorder the terms: -5x + 5x2 + -1(5 + 6x) = 5(3x + 6) -5x + 5x2 + (5 * -1 + 6x * -1) = 5(3x + 6) -5x + 5x2 + (-5 + -6x) = 5(3x + 6) Reorder the terms: -5 + -5x + -6x + 5x2 = 5(3x + 6) Combine like terms: -5x + -6x = -11x -5 + -11x + 5x2 = 5(3x + 6) Reorder the terms: -5 + -11x + 5x2 = 5(6 + 3x) -5 + -11x + 5x2 = (6 * 5 + 3x * 5) -5 + -11x + 5x2 = (30 + 15x) Solving -5 + -11x + 5x2 = 30 + 15x Solving for variable 'x'. Reorder the terms: -5 + -30 + -11x + -15x + 5x2 = 30 + 15x + -30 + -15x Combine like terms: -5 + -30 = -35 -35 + -11x + -15x + 5x2 = 30 + 15x + -30 + -15x Combine like terms: -11x + -15x = -26x -35 + -26x + 5x2 = 30 + 15x + -30 + -15x Reorder the terms: -35 + -26x + 5x2 = 30 + -30 + 15x + -15x Combine like terms: 30 + -30 = 0 -35 + -26x + 5x2 = 0 + 15x + -15x -35 + -26x + 5x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -35 + -26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + -5.2x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -5.2x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -5.2x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5.2x + x2 = 0 + 7 -5.2x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5.2x + x2 = 7 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = 7 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = 7 + 6.76 Combine like terms: 7 + 6.76 = 13.76 6.76 + -5.2x + x2 = 13.76 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 13.76 Calculate the square root of the right side: 3.709447398 Break this problem into two subproblems by setting (x + -2.6) equal to 3.709447398 and -3.709447398.Subproblem 1
x + -2.6 = 3.709447398 Simplifying x + -2.6 = 3.709447398 Reorder the terms: -2.6 + x = 3.709447398 Solving -2.6 + x = 3.709447398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 3.709447398 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 3.709447398 + 2.6 x = 3.709447398 + 2.6 Combine like terms: 3.709447398 + 2.6 = 6.309447398 x = 6.309447398 Simplifying x = 6.309447398Subproblem 2
x + -2.6 = -3.709447398 Simplifying x + -2.6 = -3.709447398 Reorder the terms: -2.6 + x = -3.709447398 Solving -2.6 + x = -3.709447398 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -3.709447398 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -3.709447398 + 2.6 x = -3.709447398 + 2.6 Combine like terms: -3.709447398 + 2.6 = -1.109447398 x = -1.109447398 Simplifying x = -1.109447398Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.309447398, -1.109447398}
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