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Simplifying 0 = 2x2 + 15x + 10 Reorder the terms: 0 = 10 + 15x + 2x2 Solving 0 = 10 + 15x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -15x + -2x2 = 10 + 15x + 2x2 + -10 + -15x + -2x2 Reorder the terms: -10 + -15x + -2x2 = 10 + -10 + 15x + -15x + 2x2 + -2x2 Combine like terms: 10 + -10 = 0 -10 + -15x + -2x2 = 0 + 15x + -15x + 2x2 + -2x2 -10 + -15x + -2x2 = 15x + -15x + 2x2 + -2x2 Combine like terms: 15x + -15x = 0 -10 + -15x + -2x2 = 0 + 2x2 + -2x2 -10 + -15x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -10 + -15x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 15x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying 10 + 15x + 2x2 = 0 Solving 10 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + 7.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 7.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 7.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7.5x + x2 = 0 + -5 7.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 7.5x + x2 = -5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -5 + 14.0625 Combine like terms: -5 + 14.0625 = 9.0625 14.0625 + 7.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + 3.75) equal to 3.010398645 and -3.010398645.Subproblem 1
x + 3.75 = 3.010398645 Simplifying x + 3.75 = 3.010398645 Reorder the terms: 3.75 + x = 3.010398645 Solving 3.75 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 3.010398645 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 3.010398645 + -3.75 x = 3.010398645 + -3.75 Combine like terms: 3.010398645 + -3.75 = -0.739601355 x = -0.739601355 Simplifying x = -0.739601355Subproblem 2
x + 3.75 = -3.010398645 Simplifying x + 3.75 = -3.010398645 Reorder the terms: 3.75 + x = -3.010398645 Solving 3.75 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -3.010398645 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -3.010398645 + -3.75 x = -3.010398645 + -3.75 Combine like terms: -3.010398645 + -3.75 = -6.760398645 x = -6.760398645 Simplifying x = -6.760398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.739601355, -6.760398645}Solution
x = {-0.739601355, -6.760398645}
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