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Simplifying 15x2 + 60x + 56 = 0 Reorder the terms: 56 + 60x + 15x2 = 0 Solving 56 + 60x + 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'. 3.733333333 + 4x + x2 = 0 Move the constant term to the right: Add '-3.733333333' to each side of the equation. 3.733333333 + 4x + -3.733333333 + x2 = 0 + -3.733333333 Reorder the terms: 3.733333333 + -3.733333333 + 4x + x2 = 0 + -3.733333333 Combine like terms: 3.733333333 + -3.733333333 = 0.000000000 0.000000000 + 4x + x2 = 0 + -3.733333333 4x + x2 = 0 + -3.733333333 Combine like terms: 0 + -3.733333333 = -3.733333333 4x + x2 = -3.733333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.733333333 + 4 Reorder the terms: 4 + 4x + x2 = -3.733333333 + 4 Combine like terms: -3.733333333 + 4 = 0.266666667 4 + 4x + x2 = 0.266666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.266666667 Calculate the square root of the right side: 0.51639778 Break this problem into two subproblems by setting (x + 2) equal to 0.51639778 and -0.51639778.Subproblem 1
x + 2 = 0.51639778 Simplifying x + 2 = 0.51639778 Reorder the terms: 2 + x = 0.51639778 Solving 2 + x = 0.51639778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.51639778 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.51639778 + -2 x = 0.51639778 + -2 Combine like terms: 0.51639778 + -2 = -1.48360222 x = -1.48360222 Simplifying x = -1.48360222Subproblem 2
x + 2 = -0.51639778 Simplifying x + 2 = -0.51639778 Reorder the terms: 2 + x = -0.51639778 Solving 2 + x = -0.51639778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.51639778 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.51639778 + -2 x = -0.51639778 + -2 Combine like terms: -0.51639778 + -2 = -2.51639778 x = -2.51639778 Simplifying x = -2.51639778Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.48360222, -2.51639778}
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