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Simplifying 10x2 + 15x + -12 = 0 Reorder the terms: -12 + 15x + 10x2 = 0 Solving -12 + 15x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.2 + 1.5x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 1.5x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 1.5x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 1.5x + x2 = 0 + 1.2 1.5x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 1.5x + x2 = 1.2 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 1.2 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1.2 + 0.5625 Combine like terms: 1.2 + 0.5625 = 1.7625 0.5625 + 1.5x + x2 = 1.7625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1.7625 Calculate the square root of the right side: 1.327591805 Break this problem into two subproblems by setting (x + 0.75) equal to 1.327591805 and -1.327591805.Subproblem 1
x + 0.75 = 1.327591805 Simplifying x + 0.75 = 1.327591805 Reorder the terms: 0.75 + x = 1.327591805 Solving 0.75 + x = 1.327591805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.327591805 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.327591805 + -0.75 x = 1.327591805 + -0.75 Combine like terms: 1.327591805 + -0.75 = 0.577591805 x = 0.577591805 Simplifying x = 0.577591805Subproblem 2
x + 0.75 = -1.327591805 Simplifying x + 0.75 = -1.327591805 Reorder the terms: 0.75 + x = -1.327591805 Solving 0.75 + x = -1.327591805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.327591805 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.327591805 + -0.75 x = -1.327591805 + -0.75 Combine like terms: -1.327591805 + -0.75 = -2.077591805 x = -2.077591805 Simplifying x = -2.077591805Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.577591805, -2.077591805}
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