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Simplifying 0 = 4.9x2 + -2x + -10 Reorder the terms: 0 = -10 + -2x + 4.9x2 Solving 0 = -10 + -2x + 4.9x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + 2x + -4.9x2 = -10 + -2x + 4.9x2 + 10 + 2x + -4.9x2 Reorder the terms: 10 + 2x + -4.9x2 = -10 + 10 + -2x + 2x + 4.9x2 + -4.9x2 Combine like terms: -10 + 10 = 0 10 + 2x + -4.9x2 = 0 + -2x + 2x + 4.9x2 + -4.9x2 10 + 2x + -4.9x2 = -2x + 2x + 4.9x2 + -4.9x2 Combine like terms: -2x + 2x = 0 10 + 2x + -4.9x2 = 0 + 4.9x2 + -4.9x2 10 + 2x + -4.9x2 = 4.9x2 + -4.9x2 Combine like terms: 4.9x2 + -4.9x2 = 0.0 10 + 2x + -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 + -0.4081632653x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -0.4081632653x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -0.4081632653x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -0.4081632653x + x2 = 0 + 2.040816327 -0.4081632653x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -0.4081632653x + x2 = 2.040816327 The x term is -0.4081632653x. Take half its coefficient (-0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. -0.4081632653x + 0.04164931281 + x2 = 2.040816327 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653x + x2 = 2.040816327 + 0.04164931281 Combine like terms: 2.040816327 + 0.04164931281 = 2.08246563981 0.04164931281 + -0.4081632653x + x2 = 2.08246563981 Factor a perfect square on the left side: (x + -0.2040816327)(x + -0.2040816327) = 2.08246563981 Calculate the square root of the right side: 1.443075064 Break this problem into two subproblems by setting (x + -0.2040816327) equal to 1.443075064 and -1.443075064.Subproblem 1
x + -0.2040816327 = 1.443075064 Simplifying x + -0.2040816327 = 1.443075064 Reorder the terms: -0.2040816327 + x = 1.443075064 Solving -0.2040816327 + x = 1.443075064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + x = 1.443075064 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + x = 1.443075064 + 0.2040816327 x = 1.443075064 + 0.2040816327 Combine like terms: 1.443075064 + 0.2040816327 = 1.6471566967 x = 1.6471566967 Simplifying x = 1.6471566967Subproblem 2
x + -0.2040816327 = -1.443075064 Simplifying x + -0.2040816327 = -1.443075064 Reorder the terms: -0.2040816327 + x = -1.443075064 Solving -0.2040816327 + x = -1.443075064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + x = -1.443075064 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + x = -1.443075064 + 0.2040816327 x = -1.443075064 + 0.2040816327 Combine like terms: -1.443075064 + 0.2040816327 = -1.2389934313 x = -1.2389934313 Simplifying x = -1.2389934313Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6471566967, -1.2389934313}
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