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Simplifying 15x2 + 14x + -60 = 0 Reorder the terms: -60 + 14x + 15x2 = 0 Solving -60 + 14x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -4 + 0.9333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.9333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.9333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.9333333333x + x2 = 0 + 4 0.9333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.9333333333x + x2 = 4 The x term is 0.9333333333x. Take half its coefficient (0.4666666667). Square it (0.2177777778) and add it to both sides. Add '0.2177777778' to each side of the equation. 0.9333333333x + 0.2177777778 + x2 = 4 + 0.2177777778 Reorder the terms: 0.2177777778 + 0.9333333333x + x2 = 4 + 0.2177777778 Combine like terms: 4 + 0.2177777778 = 4.2177777778 0.2177777778 + 0.9333333333x + x2 = 4.2177777778 Factor a perfect square on the left side: (x + 0.4666666667)(x + 0.4666666667) = 4.2177777778 Calculate the square root of the right side: 2.053722907 Break this problem into two subproblems by setting (x + 0.4666666667) equal to 2.053722907 and -2.053722907.Subproblem 1
x + 0.4666666667 = 2.053722907 Simplifying x + 0.4666666667 = 2.053722907 Reorder the terms: 0.4666666667 + x = 2.053722907 Solving 0.4666666667 + x = 2.053722907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = 2.053722907 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = 2.053722907 + -0.4666666667 x = 2.053722907 + -0.4666666667 Combine like terms: 2.053722907 + -0.4666666667 = 1.5870562403 x = 1.5870562403 Simplifying x = 1.5870562403Subproblem 2
x + 0.4666666667 = -2.053722907 Simplifying x + 0.4666666667 = -2.053722907 Reorder the terms: 0.4666666667 + x = -2.053722907 Solving 0.4666666667 + x = -2.053722907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4666666667' to each side of the equation. 0.4666666667 + -0.4666666667 + x = -2.053722907 + -0.4666666667 Combine like terms: 0.4666666667 + -0.4666666667 = 0.0000000000 0.0000000000 + x = -2.053722907 + -0.4666666667 x = -2.053722907 + -0.4666666667 Combine like terms: -2.053722907 + -0.4666666667 = -2.5203895737 x = -2.5203895737 Simplifying x = -2.5203895737Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5870562403, -2.5203895737}
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