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Simplifying 0 = 6.5 + 3x + -4.9x2 Solving 0 = 6.5 + 3x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -6.5 = -6.5 -6.5 + -3x + 4.9x2 = 6.5 + 3x + -4.9x2 + -6.5 + -3x + 4.9x2 Reorder the terms: -6.5 + -3x + 4.9x2 = 6.5 + -6.5 + 3x + -3x + -4.9x2 + 4.9x2 Combine like terms: 6.5 + -6.5 = 0.0 -6.5 + -3x + 4.9x2 = 0.0 + 3x + -3x + -4.9x2 + 4.9x2 -6.5 + -3x + 4.9x2 = 3x + -3x + -4.9x2 + 4.9x2 Combine like terms: 3x + -3x = 0 -6.5 + -3x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -6.5 + -3x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -6.5 + -3x + 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'. -1.326530612 + -0.612244898x + x2 = 0 Move the constant term to the right: Add '1.326530612' to each side of the equation. -1.326530612 + -0.612244898x + 1.326530612 + x2 = 0 + 1.326530612 Reorder the terms: -1.326530612 + 1.326530612 + -0.612244898x + x2 = 0 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + -0.612244898x + x2 = 0 + 1.326530612 -0.612244898x + x2 = 0 + 1.326530612 Combine like terms: 0 + 1.326530612 = 1.326530612 -0.612244898x + x2 = 1.326530612 The x term is -0.612244898x. Take half its coefficient (-0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. -0.612244898x + 0.09371095378 + x2 = 1.326530612 + 0.09371095378 Reorder the terms: 0.09371095378 + -0.612244898x + x2 = 1.326530612 + 0.09371095378 Combine like terms: 1.326530612 + 0.09371095378 = 1.42024156578 0.09371095378 + -0.612244898x + x2 = 1.42024156578 Factor a perfect square on the left side: (x + -0.306122449)(x + -0.306122449) = 1.42024156578 Calculate the square root of the right side: 1.191738883 Break this problem into two subproblems by setting (x + -0.306122449) equal to 1.191738883 and -1.191738883.Subproblem 1
x + -0.306122449 = 1.191738883 Simplifying x + -0.306122449 = 1.191738883 Reorder the terms: -0.306122449 + x = 1.191738883 Solving -0.306122449 + x = 1.191738883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.306122449' to each side of the equation. -0.306122449 + 0.306122449 + x = 1.191738883 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + x = 1.191738883 + 0.306122449 x = 1.191738883 + 0.306122449 Combine like terms: 1.191738883 + 0.306122449 = 1.497861332 x = 1.497861332 Simplifying x = 1.497861332Subproblem 2
x + -0.306122449 = -1.191738883 Simplifying x + -0.306122449 = -1.191738883 Reorder the terms: -0.306122449 + x = -1.191738883 Solving -0.306122449 + x = -1.191738883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.306122449' to each side of the equation. -0.306122449 + 0.306122449 + x = -1.191738883 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + x = -1.191738883 + 0.306122449 x = -1.191738883 + 0.306122449 Combine like terms: -1.191738883 + 0.306122449 = -0.885616434 x = -0.885616434 Simplifying x = -0.885616434Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.497861332, -0.885616434}
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