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Simplifying -4.9x2 + 1.5x + 5 = 0 Reorder the terms: 5 + 1.5x + -4.9x2 = 0 Solving 5 + 1.5x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -1.020408163 + -0.306122449x + x2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -0.306122449x + 1.020408163 + x2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -0.306122449x + x2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -0.306122449x + x2 = 0 + 1.020408163 -0.306122449x + x2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -0.306122449x + x2 = 1.020408163 The x term is -0.306122449x. Take half its coefficient (-0.1530612245). Square it (0.02342773845) and add it to both sides. Add '0.02342773845' to each side of the equation. -0.306122449x + 0.02342773845 + x2 = 1.020408163 + 0.02342773845 Reorder the terms: 0.02342773845 + -0.306122449x + x2 = 1.020408163 + 0.02342773845 Combine like terms: 1.020408163 + 0.02342773845 = 1.04383590145 0.02342773845 + -0.306122449x + x2 = 1.04383590145 Factor a perfect square on the left side: (x + -0.1530612245)(x + -0.1530612245) = 1.04383590145 Calculate the square root of the right side: 1.021682877 Break this problem into two subproblems by setting (x + -0.1530612245) equal to 1.021682877 and -1.021682877.Subproblem 1
x + -0.1530612245 = 1.021682877 Simplifying x + -0.1530612245 = 1.021682877 Reorder the terms: -0.1530612245 + x = 1.021682877 Solving -0.1530612245 + x = 1.021682877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + x = 1.021682877 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + x = 1.021682877 + 0.1530612245 x = 1.021682877 + 0.1530612245 Combine like terms: 1.021682877 + 0.1530612245 = 1.1747441015 x = 1.1747441015 Simplifying x = 1.1747441015Subproblem 2
x + -0.1530612245 = -1.021682877 Simplifying x + -0.1530612245 = -1.021682877 Reorder the terms: -0.1530612245 + x = -1.021682877 Solving -0.1530612245 + x = -1.021682877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + x = -1.021682877 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + x = -1.021682877 + 0.1530612245 x = -1.021682877 + 0.1530612245 Combine like terms: -1.021682877 + 0.1530612245 = -0.8686216525 x = -0.8686216525 Simplifying x = -0.8686216525Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1747441015, -0.8686216525}
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