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Simplifying 15x2 + -6x + -11 = 0 Reorder the terms: -11 + -6x + 15x2 = 0 Solving -11 + -6x + 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'. -0.7333333333 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.7333333333' to each side of the equation. -0.7333333333 + -0.4x + 0.7333333333 + x2 = 0 + 0.7333333333 Reorder the terms: -0.7333333333 + 0.7333333333 + -0.4x + x2 = 0 + 0.7333333333 Combine like terms: -0.7333333333 + 0.7333333333 = 0.0000000000 0.0000000000 + -0.4x + x2 = 0 + 0.7333333333 -0.4x + x2 = 0 + 0.7333333333 Combine like terms: 0 + 0.7333333333 = 0.7333333333 -0.4x + x2 = 0.7333333333 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.7333333333 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.7333333333 + 0.04 Combine like terms: 0.7333333333 + 0.04 = 0.7733333333 0.04 + -0.4x + x2 = 0.7733333333 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.7733333333 Calculate the square root of the right side: 0.879393731 Break this problem into two subproblems by setting (x + -0.2) equal to 0.879393731 and -0.879393731.Subproblem 1
x + -0.2 = 0.879393731 Simplifying x + -0.2 = 0.879393731 Reorder the terms: -0.2 + x = 0.879393731 Solving -0.2 + x = 0.879393731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.879393731 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.879393731 + 0.2 x = 0.879393731 + 0.2 Combine like terms: 0.879393731 + 0.2 = 1.079393731 x = 1.079393731 Simplifying x = 1.079393731Subproblem 2
x + -0.2 = -0.879393731 Simplifying x + -0.2 = -0.879393731 Reorder the terms: -0.2 + x = -0.879393731 Solving -0.2 + x = -0.879393731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.879393731 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.879393731 + 0.2 x = -0.879393731 + 0.2 Combine like terms: -0.879393731 + 0.2 = -0.679393731 x = -0.679393731 Simplifying x = -0.679393731Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.079393731, -0.679393731}
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