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Simplifying 0 = -4.9x2 + 5x + 10 Reorder the terms: 0 = 10 + 5x + -4.9x2 Solving 0 = 10 + 5x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -5x + 4.9x2 = 10 + 5x + -4.9x2 + -10 + -5x + 4.9x2 Reorder the terms: -10 + -5x + 4.9x2 = 10 + -10 + 5x + -5x + -4.9x2 + 4.9x2 Combine like terms: 10 + -10 = 0 -10 + -5x + 4.9x2 = 0 + 5x + -5x + -4.9x2 + 4.9x2 -10 + -5x + 4.9x2 = 5x + -5x + -4.9x2 + 4.9x2 Combine like terms: 5x + -5x = 0 -10 + -5x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -10 + -5x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -10 + -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'. -2.040816327 + -1.020408163x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -1.020408163x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -1.020408163x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -1.020408163x + x2 = 0 + 2.040816327 -1.020408163x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -1.020408163x + x2 = 2.040816327 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 = 2.040816327 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163x + x2 = 2.040816327 + 0.2603082048 Combine like terms: 2.040816327 + 0.2603082048 = 2.3011245318 0.2603082048 + -1.020408163x + x2 = 2.3011245318 Factor a perfect square on the left side: (x + -0.5102040815)(x + -0.5102040815) = 2.3011245318 Calculate the square root of the right side: 1.516945791 Break this problem into two subproblems by setting (x + -0.5102040815) equal to 1.516945791 and -1.516945791.Subproblem 1
x + -0.5102040815 = 1.516945791 Simplifying x + -0.5102040815 = 1.516945791 Reorder the terms: -0.5102040815 + x = 1.516945791 Solving -0.5102040815 + x = 1.516945791 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 = 1.516945791 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = 1.516945791 + 0.5102040815 x = 1.516945791 + 0.5102040815 Combine like terms: 1.516945791 + 0.5102040815 = 2.0271498725 x = 2.0271498725 Simplifying x = 2.0271498725Subproblem 2
x + -0.5102040815 = -1.516945791 Simplifying x + -0.5102040815 = -1.516945791 Reorder the terms: -0.5102040815 + x = -1.516945791 Solving -0.5102040815 + x = -1.516945791 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 = -1.516945791 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + x = -1.516945791 + 0.5102040815 x = -1.516945791 + 0.5102040815 Combine like terms: -1.516945791 + 0.5102040815 = -1.0067417095 x = -1.0067417095 Simplifying x = -1.0067417095Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0271498725, -1.0067417095}
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