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Simplifying 2.5x2 + -4.75x + 2.1 = 0 Reorder the terms: 2.1 + -4.75x + 2.5x2 = 0 Solving 2.1 + -4.75x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 0.84 + -1.9x + x2 = 0 Move the constant term to the right: Add '-0.84' to each side of the equation. 0.84 + -1.9x + -0.84 + x2 = 0 + -0.84 Reorder the terms: 0.84 + -0.84 + -1.9x + x2 = 0 + -0.84 Combine like terms: 0.84 + -0.84 = 0.00 0.00 + -1.9x + x2 = 0 + -0.84 -1.9x + x2 = 0 + -0.84 Combine like terms: 0 + -0.84 = -0.84 -1.9x + x2 = -0.84 The x term is -1.9x. Take half its coefficient (-0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. -1.9x + 0.9025 + x2 = -0.84 + 0.9025 Reorder the terms: 0.9025 + -1.9x + x2 = -0.84 + 0.9025 Combine like terms: -0.84 + 0.9025 = 0.0625 0.9025 + -1.9x + x2 = 0.0625 Factor a perfect square on the left side: (x + -0.95)(x + -0.95) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (x + -0.95) equal to 0.25 and -0.25.Subproblem 1
x + -0.95 = 0.25 Simplifying x + -0.95 = 0.25 Reorder the terms: -0.95 + x = 0.25 Solving -0.95 + x = 0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = 0.25 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = 0.25 + 0.95 x = 0.25 + 0.95 Combine like terms: 0.25 + 0.95 = 1.2 x = 1.2 Simplifying x = 1.2Subproblem 2
x + -0.95 = -0.25 Simplifying x + -0.95 = -0.25 Reorder the terms: -0.95 + x = -0.25 Solving -0.95 + x = -0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.95' to each side of the equation. -0.95 + 0.95 + x = -0.25 + 0.95 Combine like terms: -0.95 + 0.95 = 0.00 0.00 + x = -0.25 + 0.95 x = -0.25 + 0.95 Combine like terms: -0.25 + 0.95 = 0.7 x = 0.7 Simplifying x = 0.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2, 0.7}
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