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Simplifying 0 = -4.9x2 + 2.29x + 0.5 Reorder the terms: 0 = 0.5 + 2.29x + -4.9x2 Solving 0 = 0.5 + 2.29x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -0.5 = -0.5 -0.5 + -2.29x + 4.9x2 = 0.5 + 2.29x + -4.9x2 + -0.5 + -2.29x + 4.9x2 Reorder the terms: -0.5 + -2.29x + 4.9x2 = 0.5 + -0.5 + 2.29x + -2.29x + -4.9x2 + 4.9x2 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + -2.29x + 4.9x2 = 0.0 + 2.29x + -2.29x + -4.9x2 + 4.9x2 -0.5 + -2.29x + 4.9x2 = 2.29x + -2.29x + -4.9x2 + 4.9x2 Combine like terms: 2.29x + -2.29x = 0.00 -0.5 + -2.29x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 -0.5 + -2.29x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -0.5 + -2.29x + 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'. -0.1020408163 + -0.4673469388x + x2 = 0 Move the constant term to the right: Add '0.1020408163' to each side of the equation. -0.1020408163 + -0.4673469388x + 0.1020408163 + x2 = 0 + 0.1020408163 Reorder the terms: -0.1020408163 + 0.1020408163 + -0.4673469388x + x2 = 0 + 0.1020408163 Combine like terms: -0.1020408163 + 0.1020408163 = 0.0000000000 0.0000000000 + -0.4673469388x + x2 = 0 + 0.1020408163 -0.4673469388x + x2 = 0 + 0.1020408163 Combine like terms: 0 + 0.1020408163 = 0.1020408163 -0.4673469388x + x2 = 0.1020408163 The x term is -0.4673469388x. Take half its coefficient (-0.2336734694). Square it (0.05460329030) and add it to both sides. Add '0.05460329030' to each side of the equation. -0.4673469388x + 0.05460329030 + x2 = 0.1020408163 + 0.05460329030 Reorder the terms: 0.05460329030 + -0.4673469388x + x2 = 0.1020408163 + 0.05460329030 Combine like terms: 0.1020408163 + 0.05460329030 = 0.1566441066 0.05460329030 + -0.4673469388x + x2 = 0.1566441066 Factor a perfect square on the left side: (x + -0.2336734694)(x + -0.2336734694) = 0.1566441066 Calculate the square root of the right side: 0.395782903 Break this problem into two subproblems by setting (x + -0.2336734694) equal to 0.395782903 and -0.395782903.Subproblem 1
x + -0.2336734694 = 0.395782903 Simplifying x + -0.2336734694 = 0.395782903 Reorder the terms: -0.2336734694 + x = 0.395782903 Solving -0.2336734694 + x = 0.395782903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2336734694' to each side of the equation. -0.2336734694 + 0.2336734694 + x = 0.395782903 + 0.2336734694 Combine like terms: -0.2336734694 + 0.2336734694 = 0.0000000000 0.0000000000 + x = 0.395782903 + 0.2336734694 x = 0.395782903 + 0.2336734694 Combine like terms: 0.395782903 + 0.2336734694 = 0.6294563724 x = 0.6294563724 Simplifying x = 0.6294563724Subproblem 2
x + -0.2336734694 = -0.395782903 Simplifying x + -0.2336734694 = -0.395782903 Reorder the terms: -0.2336734694 + x = -0.395782903 Solving -0.2336734694 + x = -0.395782903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2336734694' to each side of the equation. -0.2336734694 + 0.2336734694 + x = -0.395782903 + 0.2336734694 Combine like terms: -0.2336734694 + 0.2336734694 = 0.0000000000 0.0000000000 + x = -0.395782903 + 0.2336734694 x = -0.395782903 + 0.2336734694 Combine like terms: -0.395782903 + 0.2336734694 = -0.1621094336 x = -0.1621094336 Simplifying x = -0.1621094336Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6294563724, -0.1621094336}
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