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Simplifying 0 = -0.083x2 + 6.4x + 3.43 Reorder the terms: 0 = 3.43 + 6.4x + -0.083x2 Solving 0 = 3.43 + 6.4x + -0.083x2 Solving for variable 'x'. Combine like terms: 0 + -3.43 = -3.43 -3.43 + -6.4x + 0.083x2 = 3.43 + 6.4x + -0.083x2 + -3.43 + -6.4x + 0.083x2 Reorder the terms: -3.43 + -6.4x + 0.083x2 = 3.43 + -3.43 + 6.4x + -6.4x + -0.083x2 + 0.083x2 Combine like terms: 3.43 + -3.43 = 0.00 -3.43 + -6.4x + 0.083x2 = 0.00 + 6.4x + -6.4x + -0.083x2 + 0.083x2 -3.43 + -6.4x + 0.083x2 = 6.4x + -6.4x + -0.083x2 + 0.083x2 Combine like terms: 6.4x + -6.4x = 0.0 -3.43 + -6.4x + 0.083x2 = 0.0 + -0.083x2 + 0.083x2 -3.43 + -6.4x + 0.083x2 = -0.083x2 + 0.083x2 Combine like terms: -0.083x2 + 0.083x2 = 0.000 -3.43 + -6.4x + 0.083x2 = 0.000 Begin completing the square. Divide all terms by 0.083 the coefficient of the squared term: Divide each side by '0.083'. -41.3253012 + -77.10843373x + x2 = 0 Move the constant term to the right: Add '41.3253012' to each side of the equation. -41.3253012 + -77.10843373x + 41.3253012 + x2 = 0 + 41.3253012 Reorder the terms: -41.3253012 + 41.3253012 + -77.10843373x + x2 = 0 + 41.3253012 Combine like terms: -41.3253012 + 41.3253012 = 0.0000000 0.0000000 + -77.10843373x + x2 = 0 + 41.3253012 -77.10843373x + x2 = 0 + 41.3253012 Combine like terms: 0 + 41.3253012 = 41.3253012 -77.10843373x + x2 = 41.3253012 The x term is -77.10843373x. Take half its coefficient (-38.55421687). Square it (1486.427638) and add it to both sides. Add '1486.427638' to each side of the equation. -77.10843373x + 1486.427638 + x2 = 41.3253012 + 1486.427638 Reorder the terms: 1486.427638 + -77.10843373x + x2 = 41.3253012 + 1486.427638 Combine like terms: 41.3253012 + 1486.427638 = 1527.7529392 1486.427638 + -77.10843373x + x2 = 1527.7529392 Factor a perfect square on the left side: (x + -38.55421687)(x + -38.55421687) = 1527.7529392 Calculate the square root of the right side: 39.086480261 Break this problem into two subproblems by setting (x + -38.55421687) equal to 39.086480261 and -39.086480261.Subproblem 1
x + -38.55421687 = 39.086480261 Simplifying x + -38.55421687 = 39.086480261 Reorder the terms: -38.55421687 + x = 39.086480261 Solving -38.55421687 + x = 39.086480261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.55421687' to each side of the equation. -38.55421687 + 38.55421687 + x = 39.086480261 + 38.55421687 Combine like terms: -38.55421687 + 38.55421687 = 0.00000000 0.00000000 + x = 39.086480261 + 38.55421687 x = 39.086480261 + 38.55421687 Combine like terms: 39.086480261 + 38.55421687 = 77.640697131 x = 77.640697131 Simplifying x = 77.640697131Subproblem 2
x + -38.55421687 = -39.086480261 Simplifying x + -38.55421687 = -39.086480261 Reorder the terms: -38.55421687 + x = -39.086480261 Solving -38.55421687 + x = -39.086480261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.55421687' to each side of the equation. -38.55421687 + 38.55421687 + x = -39.086480261 + 38.55421687 Combine like terms: -38.55421687 + 38.55421687 = 0.00000000 0.00000000 + x = -39.086480261 + 38.55421687 x = -39.086480261 + 38.55421687 Combine like terms: -39.086480261 + 38.55421687 = -0.532263391 x = -0.532263391 Simplifying x = -0.532263391Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.640697131, -0.532263391}
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