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Simplifying 6.5x2 + 4.9x + -0.25 = 0 Reorder the terms: -0.25 + 4.9x + 6.5x2 = 0 Solving -0.25 + 4.9x + 6.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.5 the coefficient of the squared term: Divide each side by '6.5'. -0.03846153846 + 0.7538461538x + x2 = 0 Move the constant term to the right: Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.7538461538x + 0.03846153846 + x2 = 0 + 0.03846153846 Reorder the terms: -0.03846153846 + 0.03846153846 + 0.7538461538x + x2 = 0 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + 0.7538461538x + x2 = 0 + 0.03846153846 0.7538461538x + x2 = 0 + 0.03846153846 Combine like terms: 0 + 0.03846153846 = 0.03846153846 0.7538461538x + x2 = 0.03846153846 The x term is 0.7538461538x. Take half its coefficient (0.3769230769). Square it (0.1420710059) and add it to both sides. Add '0.1420710059' to each side of the equation. 0.7538461538x + 0.1420710059 + x2 = 0.03846153846 + 0.1420710059 Reorder the terms: 0.1420710059 + 0.7538461538x + x2 = 0.03846153846 + 0.1420710059 Combine like terms: 0.03846153846 + 0.1420710059 = 0.18053254436 0.1420710059 + 0.7538461538x + x2 = 0.18053254436 Factor a perfect square on the left side: (x + 0.3769230769)(x + 0.3769230769) = 0.18053254436 Calculate the square root of the right side: 0.424891215 Break this problem into two subproblems by setting (x + 0.3769230769) equal to 0.424891215 and -0.424891215.Subproblem 1
x + 0.3769230769 = 0.424891215 Simplifying x + 0.3769230769 = 0.424891215 Reorder the terms: 0.3769230769 + x = 0.424891215 Solving 0.3769230769 + x = 0.424891215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3769230769' to each side of the equation. 0.3769230769 + -0.3769230769 + x = 0.424891215 + -0.3769230769 Combine like terms: 0.3769230769 + -0.3769230769 = 0.0000000000 0.0000000000 + x = 0.424891215 + -0.3769230769 x = 0.424891215 + -0.3769230769 Combine like terms: 0.424891215 + -0.3769230769 = 0.0479681381 x = 0.0479681381 Simplifying x = 0.0479681381Subproblem 2
x + 0.3769230769 = -0.424891215 Simplifying x + 0.3769230769 = -0.424891215 Reorder the terms: 0.3769230769 + x = -0.424891215 Solving 0.3769230769 + x = -0.424891215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3769230769' to each side of the equation. 0.3769230769 + -0.3769230769 + x = -0.424891215 + -0.3769230769 Combine like terms: 0.3769230769 + -0.3769230769 = 0.0000000000 0.0000000000 + x = -0.424891215 + -0.3769230769 x = -0.424891215 + -0.3769230769 Combine like terms: -0.424891215 + -0.3769230769 = -0.8018142919 x = -0.8018142919 Simplifying x = -0.8018142919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0479681381, -0.8018142919}
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