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Simplifying 6.664 = -4.9x2 + 12.25x + 0 Reorder the terms: 6.664 = 0 + 12.25x + -4.9x2 Remove the zero: 6.664 = 12.25x + -4.9x2 Solving 6.664 = 12.25x + -4.9x2 Solving for variable 'x'. Reorder the terms: 6.664 + -12.25x + 4.9x2 = 12.25x + -12.25x + -4.9x2 + 4.9x2 Combine like terms: 12.25x + -12.25x = 0.00 6.664 + -12.25x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 6.664 + -12.25x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 6.664 + -12.25x + 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'. 1.36 + -2.5x + x2 = 0 Move the constant term to the right: Add '-1.36' to each side of the equation. 1.36 + -2.5x + -1.36 + x2 = 0 + -1.36 Reorder the terms: 1.36 + -1.36 + -2.5x + x2 = 0 + -1.36 Combine like terms: 1.36 + -1.36 = 0.00 0.00 + -2.5x + x2 = 0 + -1.36 -2.5x + x2 = 0 + -1.36 Combine like terms: 0 + -1.36 = -1.36 -2.5x + x2 = -1.36 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -1.36 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.36 + 1.5625 Combine like terms: -1.36 + 1.5625 = 0.2025 1.5625 + -2.5x + x2 = 0.2025 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.2025 Calculate the square root of the right side: 0.45 Break this problem into two subproblems by setting (x + -1.25) equal to 0.45 and -0.45.Subproblem 1
x + -1.25 = 0.45 Simplifying x + -1.25 = 0.45 Reorder the terms: -1.25 + x = 0.45 Solving -1.25 + x = 0.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.45 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.45 + 1.25 x = 0.45 + 1.25 Combine like terms: 0.45 + 1.25 = 1.7 x = 1.7 Simplifying x = 1.7Subproblem 2
x + -1.25 = -0.45 Simplifying x + -1.25 = -0.45 Reorder the terms: -1.25 + x = -0.45 Solving -1.25 + x = -0.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.45 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.45 + 1.25 x = -0.45 + 1.25 Combine like terms: -0.45 + 1.25 = 0.8 x = 0.8 Simplifying x = 0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7, 0.8}
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