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Simplifying 12x2 + 15x + 4 = 0 Reorder the terms: 4 + 15x + 12x2 = 0 Solving 4 + 15x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.3333333333 + 1.25x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 1.25x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 1.25x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 1.25x + x2 = 0 + -0.3333333333 1.25x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 1.25x + x2 = -0.3333333333 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -0.3333333333 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -0.3333333333 + 0.390625 Combine like terms: -0.3333333333 + 0.390625 = 0.0572916667 0.390625 + 1.25x + x2 = 0.0572916667 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 0.0572916667 Calculate the square root of the right side: 0.239356777 Break this problem into two subproblems by setting (x + 0.625) equal to 0.239356777 and -0.239356777.Subproblem 1
x + 0.625 = 0.239356777 Simplifying x + 0.625 = 0.239356777 Reorder the terms: 0.625 + x = 0.239356777 Solving 0.625 + x = 0.239356777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.239356777 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.239356777 + -0.625 x = 0.239356777 + -0.625 Combine like terms: 0.239356777 + -0.625 = -0.385643223 x = -0.385643223 Simplifying x = -0.385643223Subproblem 2
x + 0.625 = -0.239356777 Simplifying x + 0.625 = -0.239356777 Reorder the terms: 0.625 + x = -0.239356777 Solving 0.625 + x = -0.239356777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.239356777 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.239356777 + -0.625 x = -0.239356777 + -0.625 Combine like terms: -0.239356777 + -0.625 = -0.864356777 x = -0.864356777 Simplifying x = -0.864356777Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.385643223, -0.864356777}
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