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Simplifying 4.9x2 + 3.072x + -10 = 0 Reorder the terms: -10 + 3.072x + 4.9x2 = 0 Solving -10 + 3.072x + 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 + 0.6269387755x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + 0.6269387755x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + 0.6269387755x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + 0.6269387755x + x2 = 0 + 2.040816327 0.6269387755x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 0.6269387755x + x2 = 2.040816327 The x term is 0.6269387755x. Take half its coefficient (0.3134693878). Square it (0.09826305709) and add it to both sides. Add '0.09826305709' to each side of the equation. 0.6269387755x + 0.09826305709 + x2 = 2.040816327 + 0.09826305709 Reorder the terms: 0.09826305709 + 0.6269387755x + x2 = 2.040816327 + 0.09826305709 Combine like terms: 2.040816327 + 0.09826305709 = 2.13907938409 0.09826305709 + 0.6269387755x + x2 = 2.13907938409 Factor a perfect square on the left side: (x + 0.3134693878)(x + 0.3134693878) = 2.13907938409 Calculate the square root of the right side: 1.46255919 Break this problem into two subproblems by setting (x + 0.3134693878) equal to 1.46255919 and -1.46255919.Subproblem 1
x + 0.3134693878 = 1.46255919 Simplifying x + 0.3134693878 = 1.46255919 Reorder the terms: 0.3134693878 + x = 1.46255919 Solving 0.3134693878 + x = 1.46255919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3134693878' to each side of the equation. 0.3134693878 + -0.3134693878 + x = 1.46255919 + -0.3134693878 Combine like terms: 0.3134693878 + -0.3134693878 = 0.0000000000 0.0000000000 + x = 1.46255919 + -0.3134693878 x = 1.46255919 + -0.3134693878 Combine like terms: 1.46255919 + -0.3134693878 = 1.1490898022 x = 1.1490898022 Simplifying x = 1.1490898022Subproblem 2
x + 0.3134693878 = -1.46255919 Simplifying x + 0.3134693878 = -1.46255919 Reorder the terms: 0.3134693878 + x = -1.46255919 Solving 0.3134693878 + x = -1.46255919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3134693878' to each side of the equation. 0.3134693878 + -0.3134693878 + x = -1.46255919 + -0.3134693878 Combine like terms: 0.3134693878 + -0.3134693878 = 0.0000000000 0.0000000000 + x = -1.46255919 + -0.3134693878 x = -1.46255919 + -0.3134693878 Combine like terms: -1.46255919 + -0.3134693878 = -1.7760285778 x = -1.7760285778 Simplifying x = -1.7760285778Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1490898022, -1.7760285778}
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