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Simplifying 10 + 6.4x + -4.9x2 = 0 Solving 10 + 6.4x + -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'. -2.040816327 + -1.306122449x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -1.306122449x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -1.306122449x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -1.306122449x + x2 = 0 + 2.040816327 -1.306122449x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -1.306122449x + x2 = 2.040816327 The x term is -1.306122449x. Take half its coefficient (-0.6530612245). Square it (0.4264889629) and add it to both sides. Add '0.4264889629' to each side of the equation. -1.306122449x + 0.4264889629 + x2 = 2.040816327 + 0.4264889629 Reorder the terms: 0.4264889629 + -1.306122449x + x2 = 2.040816327 + 0.4264889629 Combine like terms: 2.040816327 + 0.4264889629 = 2.4673052899 0.4264889629 + -1.306122449x + x2 = 2.4673052899 Factor a perfect square on the left side: (x + -0.6530612245)(x + -0.6530612245) = 2.4673052899 Calculate the square root of the right side: 1.570765829 Break this problem into two subproblems by setting (x + -0.6530612245) equal to 1.570765829 and -1.570765829.Subproblem 1
x + -0.6530612245 = 1.570765829 Simplifying x + -0.6530612245 = 1.570765829 Reorder the terms: -0.6530612245 + x = 1.570765829 Solving -0.6530612245 + x = 1.570765829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6530612245' to each side of the equation. -0.6530612245 + 0.6530612245 + x = 1.570765829 + 0.6530612245 Combine like terms: -0.6530612245 + 0.6530612245 = 0.0000000000 0.0000000000 + x = 1.570765829 + 0.6530612245 x = 1.570765829 + 0.6530612245 Combine like terms: 1.570765829 + 0.6530612245 = 2.2238270535 x = 2.2238270535 Simplifying x = 2.2238270535Subproblem 2
x + -0.6530612245 = -1.570765829 Simplifying x + -0.6530612245 = -1.570765829 Reorder the terms: -0.6530612245 + x = -1.570765829 Solving -0.6530612245 + x = -1.570765829 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6530612245' to each side of the equation. -0.6530612245 + 0.6530612245 + x = -1.570765829 + 0.6530612245 Combine like terms: -0.6530612245 + 0.6530612245 = 0.0000000000 0.0000000000 + x = -1.570765829 + 0.6530612245 x = -1.570765829 + 0.6530612245 Combine like terms: -1.570765829 + 0.6530612245 = -0.9177046045 x = -0.9177046045 Simplifying x = -0.9177046045Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2238270535, -0.9177046045}
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