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Simplifying -4.9x2 + 12.25x + 0 = 7.35 Reorder the terms: 0 + 12.25x + -4.9x2 = 7.35 Remove the zero: 12.25x + -4.9x2 = 7.35 Solving 12.25x + -4.9x2 = 7.35 Solving for variable 'x'. Reorder the terms: -7.35 + 12.25x + -4.9x2 = 7.35 + -7.35 Combine like terms: 7.35 + -7.35 = 0.00 -7.35 + 12.25x + -4.9x2 = 0.00 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 1.5 + -2.5x + x2 = 0.0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2.5x + -1.5 + x2 = 0.0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2.5x + x2 = 0.0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2.5x + x2 = 0.0 + -1.5 -2.5x + x2 = 0.0 + -1.5 Combine like terms: 0.0 + -1.5 = -1.5 -2.5x + x2 = -1.5 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 = -1.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.5 + 1.5625 Combine like terms: -1.5 + 1.5625 = 0.0625 1.5625 + -2.5x + x2 = 0.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (x + -1.25) equal to 0.25 and -0.25.Subproblem 1
x + -1.25 = 0.25 Simplifying x + -1.25 = 0.25 Reorder the terms: -1.25 + x = 0.25 Solving -1.25 + x = 0.25 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 = 0.25 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.25 + 1.25 x = 0.25 + 1.25 Combine like terms: 0.25 + 1.25 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + -1.25 = -0.25 Simplifying x + -1.25 = -0.25 Reorder the terms: -1.25 + x = -0.25 Solving -1.25 + x = -0.25 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 = -0.25 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.25 + 1.25 x = -0.25 + 1.25 Combine like terms: -0.25 + 1.25 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, 1}
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