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Simplifying -9x = 13 + -15x2 Solving -9x = 13 + -15x2 Solving for variable 'x'. Reorder the terms: -13 + -9x + 15x2 = 13 + -15x2 + -13 + 15x2 Reorder the terms: -13 + -9x + 15x2 = 13 + -13 + -15x2 + 15x2 Combine like terms: 13 + -13 = 0 -13 + -9x + 15x2 = 0 + -15x2 + 15x2 -13 + -9x + 15x2 = -15x2 + 15x2 Combine like terms: -15x2 + 15x2 = 0 -13 + -9x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.8666666667 + -0.6x + x2 = 0 Move the constant term to the right: Add '0.8666666667' to each side of the equation. -0.8666666667 + -0.6x + 0.8666666667 + x2 = 0 + 0.8666666667 Reorder the terms: -0.8666666667 + 0.8666666667 + -0.6x + x2 = 0 + 0.8666666667 Combine like terms: -0.8666666667 + 0.8666666667 = 0.0000000000 0.0000000000 + -0.6x + x2 = 0 + 0.8666666667 -0.6x + x2 = 0 + 0.8666666667 Combine like terms: 0 + 0.8666666667 = 0.8666666667 -0.6x + x2 = 0.8666666667 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 = 0.8666666667 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 0.8666666667 + 0.09 Combine like terms: 0.8666666667 + 0.09 = 0.9566666667 0.09 + -0.6x + x2 = 0.9566666667 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 0.9566666667 Calculate the square root of the right side: 0.978093383 Break this problem into two subproblems by setting (x + -0.3) equal to 0.978093383 and -0.978093383.Subproblem 1
x + -0.3 = 0.978093383 Simplifying x + -0.3 = 0.978093383 Reorder the terms: -0.3 + x = 0.978093383 Solving -0.3 + x = 0.978093383 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 = 0.978093383 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.978093383 + 0.3 x = 0.978093383 + 0.3 Combine like terms: 0.978093383 + 0.3 = 1.278093383 x = 1.278093383 Simplifying x = 1.278093383Subproblem 2
x + -0.3 = -0.978093383 Simplifying x + -0.3 = -0.978093383 Reorder the terms: -0.3 + x = -0.978093383 Solving -0.3 + x = -0.978093383 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 = -0.978093383 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.978093383 + 0.3 x = -0.978093383 + 0.3 Combine like terms: -0.978093383 + 0.3 = -0.678093383 x = -0.678093383 Simplifying x = -0.678093383Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.278093383, -0.678093383}
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