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Simplifying 5x(x + -9) = 2x + 15 Reorder the terms: 5x(-9 + x) = 2x + 15 (-9 * 5x + x * 5x) = 2x + 15 (-45x + 5x2) = 2x + 15 Reorder the terms: -45x + 5x2 = 15 + 2x Solving -45x + 5x2 = 15 + 2x Solving for variable 'x'. Reorder the terms: -15 + -45x + -2x + 5x2 = 15 + 2x + -15 + -2x Combine like terms: -45x + -2x = -47x -15 + -47x + 5x2 = 15 + 2x + -15 + -2x Reorder the terms: -15 + -47x + 5x2 = 15 + -15 + 2x + -2x Combine like terms: 15 + -15 = 0 -15 + -47x + 5x2 = 0 + 2x + -2x -15 + -47x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -15 + -47x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + -9.4x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -9.4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -9.4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -9.4x + x2 = 0 + 3 -9.4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -9.4x + x2 = 3 The x term is -9.4x. Take half its coefficient (-4.7). Square it (22.09) and add it to both sides. Add '22.09' to each side of the equation. -9.4x + 22.09 + x2 = 3 + 22.09 Reorder the terms: 22.09 + -9.4x + x2 = 3 + 22.09 Combine like terms: 3 + 22.09 = 25.09 22.09 + -9.4x + x2 = 25.09 Factor a perfect square on the left side: (x + -4.7)(x + -4.7) = 25.09 Calculate the square root of the right side: 5.008991915 Break this problem into two subproblems by setting (x + -4.7) equal to 5.008991915 and -5.008991915.Subproblem 1
x + -4.7 = 5.008991915 Simplifying x + -4.7 = 5.008991915 Reorder the terms: -4.7 + x = 5.008991915 Solving -4.7 + x = 5.008991915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + x = 5.008991915 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + x = 5.008991915 + 4.7 x = 5.008991915 + 4.7 Combine like terms: 5.008991915 + 4.7 = 9.708991915 x = 9.708991915 Simplifying x = 9.708991915Subproblem 2
x + -4.7 = -5.008991915 Simplifying x + -4.7 = -5.008991915 Reorder the terms: -4.7 + x = -5.008991915 Solving -4.7 + x = -5.008991915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + x = -5.008991915 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + x = -5.008991915 + 4.7 x = -5.008991915 + 4.7 Combine like terms: -5.008991915 + 4.7 = -0.308991915 x = -0.308991915 Simplifying x = -0.308991915Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.708991915, -0.308991915}
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