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Simplifying 10x2 + 15x = -1 Reorder the terms: 15x + 10x2 = -1 Solving 15x + 10x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 15x + 10x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 15x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.1 + 1.5x + x2 = 0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 1.5x + -0.1 + x2 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + 1.5x + x2 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 1.5x + x2 = 0 + -0.1 1.5x + x2 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 1.5x + x2 = -0.1 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 = -0.1 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -0.1 + 0.5625 Combine like terms: -0.1 + 0.5625 = 0.4625 0.5625 + 1.5x + x2 = 0.4625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.4625 Calculate the square root of the right side: 0.680073525 Break this problem into two subproblems by setting (x + 0.75) equal to 0.680073525 and -0.680073525.Subproblem 1
x + 0.75 = 0.680073525 Simplifying x + 0.75 = 0.680073525 Reorder the terms: 0.75 + x = 0.680073525 Solving 0.75 + x = 0.680073525 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 = 0.680073525 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.680073525 + -0.75 x = 0.680073525 + -0.75 Combine like terms: 0.680073525 + -0.75 = -0.069926475 x = -0.069926475 Simplifying x = -0.069926475Subproblem 2
x + 0.75 = -0.680073525 Simplifying x + 0.75 = -0.680073525 Reorder the terms: 0.75 + x = -0.680073525 Solving 0.75 + x = -0.680073525 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 = -0.680073525 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.680073525 + -0.75 x = -0.680073525 + -0.75 Combine like terms: -0.680073525 + -0.75 = -1.430073525 x = -1.430073525 Simplifying x = -1.430073525Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.069926475, -1.430073525}
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