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Simplifying 2.5x2 + 6x + -15 = 0 Reorder the terms: -15 + 6x + 2.5x2 = 0 Solving -15 + 6x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -6 + 2.4x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 2.4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 2.4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2.4x + x2 = 0 + 6 2.4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 2.4x + x2 = 6 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 6 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 6 + 1.44 Combine like terms: 6 + 1.44 = 7.44 1.44 + 2.4x + x2 = 7.44 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 7.44 Calculate the square root of the right side: 2.727636339 Break this problem into two subproblems by setting (x + 1.2) equal to 2.727636339 and -2.727636339.Subproblem 1
x + 1.2 = 2.727636339 Simplifying x + 1.2 = 2.727636339 Reorder the terms: 1.2 + x = 2.727636339 Solving 1.2 + x = 2.727636339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 2.727636339 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 2.727636339 + -1.2 x = 2.727636339 + -1.2 Combine like terms: 2.727636339 + -1.2 = 1.527636339 x = 1.527636339 Simplifying x = 1.527636339Subproblem 2
x + 1.2 = -2.727636339 Simplifying x + 1.2 = -2.727636339 Reorder the terms: 1.2 + x = -2.727636339 Solving 1.2 + x = -2.727636339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -2.727636339 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -2.727636339 + -1.2 x = -2.727636339 + -1.2 Combine like terms: -2.727636339 + -1.2 = -3.927636339 x = -3.927636339 Simplifying x = -3.927636339Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.527636339, -3.927636339}
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