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Simplifying 15x2 + -9x = 94 Reorder the terms: -9x + 15x2 = 94 Solving -9x + 15x2 = 94 Solving for variable 'x'. Reorder the terms: -94 + -9x + 15x2 = 94 + -94 Combine like terms: 94 + -94 = 0 -94 + -9x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -6.266666667 + -0.6x + x2 = 0 Move the constant term to the right: Add '6.266666667' to each side of the equation. -6.266666667 + -0.6x + 6.266666667 + x2 = 0 + 6.266666667 Reorder the terms: -6.266666667 + 6.266666667 + -0.6x + x2 = 0 + 6.266666667 Combine like terms: -6.266666667 + 6.266666667 = 0.000000000 0.000000000 + -0.6x + x2 = 0 + 6.266666667 -0.6x + x2 = 0 + 6.266666667 Combine like terms: 0 + 6.266666667 = 6.266666667 -0.6x + x2 = 6.266666667 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 = 6.266666667 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 6.266666667 + 0.09 Combine like terms: 6.266666667 + 0.09 = 6.356666667 0.09 + -0.6x + x2 = 6.356666667 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 6.356666667 Calculate the square root of the right side: 2.52124308 Break this problem into two subproblems by setting (x + -0.3) equal to 2.52124308 and -2.52124308.Subproblem 1
x + -0.3 = 2.52124308 Simplifying x + -0.3 = 2.52124308 Reorder the terms: -0.3 + x = 2.52124308 Solving -0.3 + x = 2.52124308 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 = 2.52124308 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 2.52124308 + 0.3 x = 2.52124308 + 0.3 Combine like terms: 2.52124308 + 0.3 = 2.82124308 x = 2.82124308 Simplifying x = 2.82124308Subproblem 2
x + -0.3 = -2.52124308 Simplifying x + -0.3 = -2.52124308 Reorder the terms: -0.3 + x = -2.52124308 Solving -0.3 + x = -2.52124308 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 = -2.52124308 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -2.52124308 + 0.3 x = -2.52124308 + 0.3 Combine like terms: -2.52124308 + 0.3 = -2.22124308 x = -2.22124308 Simplifying x = -2.22124308Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.82124308, -2.22124308}
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