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Simplifying 5x2 + 30x + 32 = 0 Reorder the terms: 32 + 30x + 5x2 = 0 Solving 32 + 30x + 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'. 6.4 + 6x + x2 = 0 Move the constant term to the right: Add '-6.4' to each side of the equation. 6.4 + 6x + -6.4 + x2 = 0 + -6.4 Reorder the terms: 6.4 + -6.4 + 6x + x2 = 0 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + 6x + x2 = 0 + -6.4 6x + x2 = 0 + -6.4 Combine like terms: 0 + -6.4 = -6.4 6x + x2 = -6.4 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -6.4 + 9 Reorder the terms: 9 + 6x + x2 = -6.4 + 9 Combine like terms: -6.4 + 9 = 2.6 9 + 6x + x2 = 2.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 2.6 Calculate the square root of the right side: 1.61245155 Break this problem into two subproblems by setting (x + 3) equal to 1.61245155 and -1.61245155.Subproblem 1
x + 3 = 1.61245155 Simplifying x + 3 = 1.61245155 Reorder the terms: 3 + x = 1.61245155 Solving 3 + x = 1.61245155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.61245155 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.61245155 + -3 x = 1.61245155 + -3 Combine like terms: 1.61245155 + -3 = -1.38754845 x = -1.38754845 Simplifying x = -1.38754845Subproblem 2
x + 3 = -1.61245155 Simplifying x + 3 = -1.61245155 Reorder the terms: 3 + x = -1.61245155 Solving 3 + x = -1.61245155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.61245155 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.61245155 + -3 x = -1.61245155 + -3 Combine like terms: -1.61245155 + -3 = -4.61245155 x = -4.61245155 Simplifying x = -4.61245155Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.38754845, -4.61245155}
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