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Simplifying -28.3 = -2.55x + -4.9x2 Solving -28.3 = -2.55x + -4.9x2 Solving for variable 'x'. Reorder the terms: -28.3 + 2.55x + 4.9x2 = -2.55x + 2.55x + -4.9x2 + 4.9x2 Combine like terms: -2.55x + 2.55x = 0.00 -28.3 + 2.55x + 4.9x2 = 0.00 + -4.9x2 + 4.9x2 -28.3 + 2.55x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -28.3 + 2.55x + 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'. -5.775510204 + 0.5204081633x + x2 = 0 Move the constant term to the right: Add '5.775510204' to each side of the equation. -5.775510204 + 0.5204081633x + 5.775510204 + x2 = 0 + 5.775510204 Reorder the terms: -5.775510204 + 5.775510204 + 0.5204081633x + x2 = 0 + 5.775510204 Combine like terms: -5.775510204 + 5.775510204 = 0.000000000 0.000000000 + 0.5204081633x + x2 = 0 + 5.775510204 0.5204081633x + x2 = 0 + 5.775510204 Combine like terms: 0 + 5.775510204 = 5.775510204 0.5204081633x + x2 = 5.775510204 The x term is 0.5204081633x. Take half its coefficient (0.2602040817). Square it (0.06770616413) and add it to both sides. Add '0.06770616413' to each side of the equation. 0.5204081633x + 0.06770616413 + x2 = 5.775510204 + 0.06770616413 Reorder the terms: 0.06770616413 + 0.5204081633x + x2 = 5.775510204 + 0.06770616413 Combine like terms: 5.775510204 + 0.06770616413 = 5.84321636813 0.06770616413 + 0.5204081633x + x2 = 5.84321636813 Factor a perfect square on the left side: (x + 0.2602040817)(x + 0.2602040817) = 5.84321636813 Calculate the square root of the right side: 2.417274574 Break this problem into two subproblems by setting (x + 0.2602040817) equal to 2.417274574 and -2.417274574.Subproblem 1
x + 0.2602040817 = 2.417274574 Simplifying x + 0.2602040817 = 2.417274574 Reorder the terms: 0.2602040817 + x = 2.417274574 Solving 0.2602040817 + x = 2.417274574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2602040817' to each side of the equation. 0.2602040817 + -0.2602040817 + x = 2.417274574 + -0.2602040817 Combine like terms: 0.2602040817 + -0.2602040817 = 0.0000000000 0.0000000000 + x = 2.417274574 + -0.2602040817 x = 2.417274574 + -0.2602040817 Combine like terms: 2.417274574 + -0.2602040817 = 2.1570704923 x = 2.1570704923 Simplifying x = 2.1570704923Subproblem 2
x + 0.2602040817 = -2.417274574 Simplifying x + 0.2602040817 = -2.417274574 Reorder the terms: 0.2602040817 + x = -2.417274574 Solving 0.2602040817 + x = -2.417274574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2602040817' to each side of the equation. 0.2602040817 + -0.2602040817 + x = -2.417274574 + -0.2602040817 Combine like terms: 0.2602040817 + -0.2602040817 = 0.0000000000 0.0000000000 + x = -2.417274574 + -0.2602040817 x = -2.417274574 + -0.2602040817 Combine like terms: -2.417274574 + -0.2602040817 = -2.6774786557 x = -2.6774786557 Simplifying x = -2.6774786557Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1570704923, -2.6774786557}
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