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Simplifying 5x2 + 36x + 10 = 0 Reorder the terms: 10 + 36x + 5x2 = 0 Solving 10 + 36x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 7.2x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 7.2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 7.2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7.2x + x2 = 0 + -2 7.2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 7.2x + x2 = -2 The x term is 7.2x. Take half its coefficient (3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. 7.2x + 12.96 + x2 = -2 + 12.96 Reorder the terms: 12.96 + 7.2x + x2 = -2 + 12.96 Combine like terms: -2 + 12.96 = 10.96 12.96 + 7.2x + x2 = 10.96 Factor a perfect square on the left side: (x + 3.6)(x + 3.6) = 10.96 Calculate the square root of the right side: 3.310589071 Break this problem into two subproblems by setting (x + 3.6) equal to 3.310589071 and -3.310589071.Subproblem 1
x + 3.6 = 3.310589071 Simplifying x + 3.6 = 3.310589071 Reorder the terms: 3.6 + x = 3.310589071 Solving 3.6 + x = 3.310589071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = 3.310589071 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = 3.310589071 + -3.6 x = 3.310589071 + -3.6 Combine like terms: 3.310589071 + -3.6 = -0.289410929 x = -0.289410929 Simplifying x = -0.289410929Subproblem 2
x + 3.6 = -3.310589071 Simplifying x + 3.6 = -3.310589071 Reorder the terms: 3.6 + x = -3.310589071 Solving 3.6 + x = -3.310589071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = -3.310589071 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = -3.310589071 + -3.6 x = -3.310589071 + -3.6 Combine like terms: -3.310589071 + -3.6 = -6.910589071 x = -6.910589071 Simplifying x = -6.910589071Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.289410929, -6.910589071}
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