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Simplifying 25x2 + -15x + -6 = 0 Reorder the terms: -6 + -15x + 25x2 = 0 Solving -6 + -15x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.24 + -0.6x + x2 = 0 Move the constant term to the right: Add '0.24' to each side of the equation. -0.24 + -0.6x + 0.24 + x2 = 0 + 0.24 Reorder the terms: -0.24 + 0.24 + -0.6x + x2 = 0 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + -0.6x + x2 = 0 + 0.24 -0.6x + x2 = 0 + 0.24 Combine like terms: 0 + 0.24 = 0.24 -0.6x + x2 = 0.24 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 0.24 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.24 + 0.09 Combine like terms: 0.24 + 0.09 = 0.33 0.09 + -0.6x + x2 = 0.33 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.33 Calculate the square root of the right side: 0.574456265 Break this problem into two subproblems by setting (x + -0.3) equal to 0.574456265 and -0.574456265.Subproblem 1
x + -0.3 = 0.574456265 Simplifying x + -0.3 = 0.574456265 Reorder the terms: -0.3 + x = 0.574456265 Solving -0.3 + x = 0.574456265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.574456265 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.574456265 + 0.3 x = 0.574456265 + 0.3 Combine like terms: 0.574456265 + 0.3 = 0.874456265 x = 0.874456265 Simplifying x = 0.874456265Subproblem 2
x + -0.3 = -0.574456265 Simplifying x + -0.3 = -0.574456265 Reorder the terms: -0.3 + x = -0.574456265 Solving -0.3 + x = -0.574456265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.574456265 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.574456265 + 0.3 x = -0.574456265 + 0.3 Combine like terms: -0.574456265 + 0.3 = -0.274456265 x = -0.274456265 Simplifying x = -0.274456265Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.874456265, -0.274456265}
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