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Simplifying 5x2 + 4x + -84 = 0 Reorder the terms: -84 + 4x + 5x2 = 0 Solving -84 + 4x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16.8 + 0.8x + x2 = 0 Move the constant term to the right: Add '16.8' to each side of the equation. -16.8 + 0.8x + 16.8 + x2 = 0 + 16.8 Reorder the terms: -16.8 + 16.8 + 0.8x + x2 = 0 + 16.8 Combine like terms: -16.8 + 16.8 = 0.0 0.0 + 0.8x + x2 = 0 + 16.8 0.8x + x2 = 0 + 16.8 Combine like terms: 0 + 16.8 = 16.8 0.8x + x2 = 16.8 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 16.8 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 16.8 + 0.16 Combine like terms: 16.8 + 0.16 = 16.96 0.16 + 0.8x + x2 = 16.96 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 16.96 Calculate the square root of the right side: 4.118252056 Break this problem into two subproblems by setting (x + 0.4) equal to 4.118252056 and -4.118252056.Subproblem 1
x + 0.4 = 4.118252056 Simplifying x + 0.4 = 4.118252056 Reorder the terms: 0.4 + x = 4.118252056 Solving 0.4 + x = 4.118252056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 4.118252056 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 4.118252056 + -0.4 x = 4.118252056 + -0.4 Combine like terms: 4.118252056 + -0.4 = 3.718252056 x = 3.718252056 Simplifying x = 3.718252056Subproblem 2
x + 0.4 = -4.118252056 Simplifying x + 0.4 = -4.118252056 Reorder the terms: 0.4 + x = -4.118252056 Solving 0.4 + x = -4.118252056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -4.118252056 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -4.118252056 + -0.4 x = -4.118252056 + -0.4 Combine like terms: -4.118252056 + -0.4 = -4.518252056 x = -4.518252056 Simplifying x = -4.518252056Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.718252056, -4.518252056}
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