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Simplifying 15x2 + 24x + 2 = 0 Reorder the terms: 2 + 24x + 15x2 = 0 Solving 2 + 24x + 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'. 0.1333333333 + 1.6x + x2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + 1.6x + -0.1333333333 + x2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + 1.6x + x2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + 1.6x + x2 = 0 + -0.1333333333 1.6x + x2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 1.6x + x2 = -0.1333333333 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = -0.1333333333 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = -0.1333333333 + 0.64 Combine like terms: -0.1333333333 + 0.64 = 0.5066666667 0.64 + 1.6x + x2 = 0.5066666667 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 0.5066666667 Calculate the square root of the right side: 0.711805217 Break this problem into two subproblems by setting (x + 0.8) equal to 0.711805217 and -0.711805217.Subproblem 1
x + 0.8 = 0.711805217 Simplifying x + 0.8 = 0.711805217 Reorder the terms: 0.8 + x = 0.711805217 Solving 0.8 + x = 0.711805217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 0.711805217 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 0.711805217 + -0.8 x = 0.711805217 + -0.8 Combine like terms: 0.711805217 + -0.8 = -0.088194783 x = -0.088194783 Simplifying x = -0.088194783Subproblem 2
x + 0.8 = -0.711805217 Simplifying x + 0.8 = -0.711805217 Reorder the terms: 0.8 + x = -0.711805217 Solving 0.8 + x = -0.711805217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -0.711805217 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -0.711805217 + -0.8 x = -0.711805217 + -0.8 Combine like terms: -0.711805217 + -0.8 = -1.511805217 x = -1.511805217 Simplifying x = -1.511805217Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.088194783, -1.511805217}
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