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Simplifying 9x2 + -5x = 15 Reorder the terms: -5x + 9x2 = 15 Solving -5x + 9x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -5x + 9x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.666666667 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -0.5555555556x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -0.5555555556x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -0.5555555556x + x2 = 0 + 1.666666667 -0.5555555556x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -0.5555555556x + x2 = 1.666666667 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = 1.666666667 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 1.666666667 + 0.07716049384 Combine like terms: 1.666666667 + 0.07716049384 = 1.74382716084 0.07716049384 + -0.5555555556x + x2 = 1.74382716084 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 1.74382716084 Calculate the square root of the right side: 1.320540481 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 1.320540481 and -1.320540481.Subproblem 1
x + -0.2777777778 = 1.320540481 Simplifying x + -0.2777777778 = 1.320540481 Reorder the terms: -0.2777777778 + x = 1.320540481 Solving -0.2777777778 + x = 1.320540481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = 1.320540481 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 1.320540481 + 0.2777777778 x = 1.320540481 + 0.2777777778 Combine like terms: 1.320540481 + 0.2777777778 = 1.5983182588 x = 1.5983182588 Simplifying x = 1.5983182588Subproblem 2
x + -0.2777777778 = -1.320540481 Simplifying x + -0.2777777778 = -1.320540481 Reorder the terms: -0.2777777778 + x = -1.320540481 Solving -0.2777777778 + x = -1.320540481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = -1.320540481 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -1.320540481 + 0.2777777778 x = -1.320540481 + 0.2777777778 Combine like terms: -1.320540481 + 0.2777777778 = -1.0427627032 x = -1.0427627032 Simplifying x = -1.0427627032Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5983182588, -1.0427627032}
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