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Simplifying -4.9x2 + 17x + -8 = 0 Reorder the terms: -8 + 17x + -4.9x2 = 0 Solving -8 + 17x + -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'. 1.632653061 + -3.469387755x + x2 = 0 Move the constant term to the right: Add '-1.632653061' to each side of the equation. 1.632653061 + -3.469387755x + -1.632653061 + x2 = 0 + -1.632653061 Reorder the terms: 1.632653061 + -1.632653061 + -3.469387755x + x2 = 0 + -1.632653061 Combine like terms: 1.632653061 + -1.632653061 = 0.000000000 0.000000000 + -3.469387755x + x2 = 0 + -1.632653061 -3.469387755x + x2 = 0 + -1.632653061 Combine like terms: 0 + -1.632653061 = -1.632653061 -3.469387755x + x2 = -1.632653061 The x term is -3.469387755x. Take half its coefficient (-1.734693878). Square it (3.009162850) and add it to both sides. Add '3.009162850' to each side of the equation. -3.469387755x + 3.009162850 + x2 = -1.632653061 + 3.009162850 Reorder the terms: 3.009162850 + -3.469387755x + x2 = -1.632653061 + 3.009162850 Combine like terms: -1.632653061 + 3.009162850 = 1.376509789 3.009162850 + -3.469387755x + x2 = 1.376509789 Factor a perfect square on the left side: (x + -1.734693878)(x + -1.734693878) = 1.376509789 Calculate the square root of the right side: 1.17324754 Break this problem into two subproblems by setting (x + -1.734693878) equal to 1.17324754 and -1.17324754.Subproblem 1
x + -1.734693878 = 1.17324754 Simplifying x + -1.734693878 = 1.17324754 Reorder the terms: -1.734693878 + x = 1.17324754 Solving -1.734693878 + x = 1.17324754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + x = 1.17324754 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + x = 1.17324754 + 1.734693878 x = 1.17324754 + 1.734693878 Combine like terms: 1.17324754 + 1.734693878 = 2.907941418 x = 2.907941418 Simplifying x = 2.907941418Subproblem 2
x + -1.734693878 = -1.17324754 Simplifying x + -1.734693878 = -1.17324754 Reorder the terms: -1.734693878 + x = -1.17324754 Solving -1.734693878 + x = -1.17324754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + x = -1.17324754 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + x = -1.17324754 + 1.734693878 x = -1.17324754 + 1.734693878 Combine like terms: -1.17324754 + 1.734693878 = 0.561446338 x = 0.561446338 Simplifying x = 0.561446338Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.907941418, 0.561446338}
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