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Simplifying 4.9x2 + 20x + 10 = 0 Reorder the terms: 10 + 20x + 4.9x2 = 0 Solving 10 + 20x + 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 + 4.081632653x + x2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + 4.081632653x + -2.040816327 + x2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + 4.081632653x + x2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + 4.081632653x + x2 = 0 + -2.040816327 4.081632653x + x2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 4.081632653x + x2 = -2.040816327 The x term is 4.081632653x. Take half its coefficient (2.040816327). Square it (4.164931281) and add it to both sides. Add '4.164931281' to each side of the equation. 4.081632653x + 4.164931281 + x2 = -2.040816327 + 4.164931281 Reorder the terms: 4.164931281 + 4.081632653x + x2 = -2.040816327 + 4.164931281 Combine like terms: -2.040816327 + 4.164931281 = 2.124114954 4.164931281 + 4.081632653x + x2 = 2.124114954 Factor a perfect square on the left side: (x + 2.040816327)(x + 2.040816327) = 2.124114954 Calculate the square root of the right side: 1.457434374 Break this problem into two subproblems by setting (x + 2.040816327) equal to 1.457434374 and -1.457434374.Subproblem 1
x + 2.040816327 = 1.457434374 Simplifying x + 2.040816327 = 1.457434374 Reorder the terms: 2.040816327 + x = 1.457434374 Solving 2.040816327 + x = 1.457434374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + x = 1.457434374 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = 1.457434374 + -2.040816327 x = 1.457434374 + -2.040816327 Combine like terms: 1.457434374 + -2.040816327 = -0.583381953 x = -0.583381953 Simplifying x = -0.583381953Subproblem 2
x + 2.040816327 = -1.457434374 Simplifying x + 2.040816327 = -1.457434374 Reorder the terms: 2.040816327 + x = -1.457434374 Solving 2.040816327 + x = -1.457434374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.040816327' to each side of the equation. 2.040816327 + -2.040816327 + x = -1.457434374 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + x = -1.457434374 + -2.040816327 x = -1.457434374 + -2.040816327 Combine like terms: -1.457434374 + -2.040816327 = -3.498250701 x = -3.498250701 Simplifying x = -3.498250701Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.583381953, -3.498250701}
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