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Simplifying 15(x) = -4.9x2 + 10x + 40 Reorder the terms: 15x = 40 + 10x + -4.9x2 Solving 15x = 40 + 10x + -4.9x2 Solving for variable 'x'. Reorder the terms: -40 + 15x + -10x + 4.9x2 = 40 + 10x + -4.9x2 + -40 + -10x + 4.9x2 Combine like terms: 15x + -10x = 5x -40 + 5x + 4.9x2 = 40 + 10x + -4.9x2 + -40 + -10x + 4.9x2 Reorder the terms: -40 + 5x + 4.9x2 = 40 + -40 + 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 40 + -40 = 0 -40 + 5x + 4.9x2 = 0 + 10x + -10x + -4.9x2 + 4.9x2 -40 + 5x + 4.9x2 = 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 10x + -10x = 0 -40 + 5x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -40 + 5x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -40 + 5x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -8.163265306 + 1.020408163x + x2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + 1.020408163x + 8.163265306 + x2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + 1.020408163x + x2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + 1.020408163x + x2 = 0 + 8.163265306 1.020408163x + x2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 1.020408163x + x2 = 8.163265306 The x term is 1.020408163x. Take half its coefficient (0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. 1.020408163x + 0.2603082048 + x2 = 8.163265306 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163x + x2 = 8.163265306 + 0.2603082048 Combine like terms: 8.163265306 + 0.2603082048 = 8.4235735108 0.2603082048 + 1.020408163x + x2 = 8.4235735108 Factor a perfect square on the left side: (x + 0.5102040815)(x + 0.5102040815) = 8.4235735108 Calculate the square root of the right side: 2.902339317 Break this problem into two subproblems by setting (x + 0.5102040815) equal to 2.902339317 and -2.902339317.Subproblem 1
x + 0.5102040815 = 2.902339317 Simplifying x + 0.5102040815 = 2.902339317 Reorder the terms: 0.5102040815 + x = 2.902339317 Solving 0.5102040815 + x = 2.902339317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + x = 2.902339317 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = 2.902339317 + -0.5102040815 x = 2.902339317 + -0.5102040815 Combine like terms: 2.902339317 + -0.5102040815 = 2.3921352355 x = 2.3921352355 Simplifying x = 2.3921352355Subproblem 2
x + 0.5102040815 = -2.902339317 Simplifying x + 0.5102040815 = -2.902339317 Reorder the terms: 0.5102040815 + x = -2.902339317 Solving 0.5102040815 + x = -2.902339317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + x = -2.902339317 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + x = -2.902339317 + -0.5102040815 x = -2.902339317 + -0.5102040815 Combine like terms: -2.902339317 + -0.5102040815 = -3.4125433985 x = -3.4125433985 Simplifying x = -3.4125433985Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3921352355, -3.4125433985}
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