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Simplifying 5x2 + 14x = 8 Reorder the terms: 14x + 5x2 = 8 Solving 14x + 5x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 14x + 5x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 2.8x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 2.8x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 2.8x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 2.8x + x2 = 0 + 1.6 2.8x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 2.8x + x2 = 1.6 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = 1.6 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 1.6 + 1.96 Combine like terms: 1.6 + 1.96 = 3.56 1.96 + 2.8x + x2 = 3.56 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 3.56 Calculate the square root of the right side: 1.886796226 Break this problem into two subproblems by setting (x + 1.4) equal to 1.886796226 and -1.886796226.Subproblem 1
x + 1.4 = 1.886796226 Simplifying x + 1.4 = 1.886796226 Reorder the terms: 1.4 + x = 1.886796226 Solving 1.4 + x = 1.886796226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 1.886796226 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 1.886796226 + -1.4 x = 1.886796226 + -1.4 Combine like terms: 1.886796226 + -1.4 = 0.486796226 x = 0.486796226 Simplifying x = 0.486796226Subproblem 2
x + 1.4 = -1.886796226 Simplifying x + 1.4 = -1.886796226 Reorder the terms: 1.4 + x = -1.886796226 Solving 1.4 + x = -1.886796226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -1.886796226 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -1.886796226 + -1.4 x = -1.886796226 + -1.4 Combine like terms: -1.886796226 + -1.4 = -3.286796226 x = -3.286796226 Simplifying x = -3.286796226Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.486796226, -3.286796226}
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