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Simplifying 4.9x2 + 5x + -10 = 0 Reorder the terms: -10 + 5x + 4.9x2 = 0 Solving -10 + 5x + 4.9x2 = 0 Solving for variable 'x'. 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 = 1.0067417095 x = 1.0067417095 Simplifying x = 1.0067417095Subproblem 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 = -2.0271498725 x = -2.0271498725 Simplifying x = -2.0271498725Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0067417095, -2.0271498725}
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