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Simplifying 5x + 14 = 5(x2 + -36) Reorder the terms: 14 + 5x = 5(x2 + -36) Reorder the terms: 14 + 5x = 5(-36 + x2) 14 + 5x = (-36 * 5 + x2 * 5) 14 + 5x = (-180 + 5x2) Solving 14 + 5x = -180 + 5x2 Solving for variable 'x'. Reorder the terms: 14 + 180 + 5x + -5x2 = -180 + 5x2 + 180 + -5x2 Combine like terms: 14 + 180 = 194 194 + 5x + -5x2 = -180 + 5x2 + 180 + -5x2 Reorder the terms: 194 + 5x + -5x2 = -180 + 180 + 5x2 + -5x2 Combine like terms: -180 + 180 = 0 194 + 5x + -5x2 = 0 + 5x2 + -5x2 194 + 5x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 194 + 5x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -38.8 + -1x + x2 = 0 Move the constant term to the right: Add '38.8' to each side of the equation. -38.8 + -1x + 38.8 + x2 = 0 + 38.8 Reorder the terms: -38.8 + 38.8 + -1x + x2 = 0 + 38.8 Combine like terms: -38.8 + 38.8 = 0.0 0.0 + -1x + x2 = 0 + 38.8 -1x + x2 = 0 + 38.8 Combine like terms: 0 + 38.8 = 38.8 -1x + x2 = 38.8 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 38.8 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 38.8 + 0.25 Combine like terms: 38.8 + 0.25 = 39.05 0.25 + -1x + x2 = 39.05 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 39.05 Calculate the square root of the right side: 6.24899992 Break this problem into two subproblems by setting (x + -0.5) equal to 6.24899992 and -6.24899992.Subproblem 1
x + -0.5 = 6.24899992 Simplifying x + -0.5 = 6.24899992 Reorder the terms: -0.5 + x = 6.24899992 Solving -0.5 + x = 6.24899992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 6.24899992 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.24899992 + 0.5 x = 6.24899992 + 0.5 Combine like terms: 6.24899992 + 0.5 = 6.74899992 x = 6.74899992 Simplifying x = 6.74899992Subproblem 2
x + -0.5 = -6.24899992 Simplifying x + -0.5 = -6.24899992 Reorder the terms: -0.5 + x = -6.24899992 Solving -0.5 + x = -6.24899992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -6.24899992 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.24899992 + 0.5 x = -6.24899992 + 0.5 Combine like terms: -6.24899992 + 0.5 = -5.74899992 x = -5.74899992 Simplifying x = -5.74899992Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.74899992, -5.74899992}
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