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Simplifying 5x2 + 9.8 = 14x Reorder the terms: 9.8 + 5x2 = 14x Solving 9.8 + 5x2 = 14x Solving for variable 'x'. Reorder the terms: 9.8 + -14x + 5x2 = 14x + -14x Combine like terms: 14x + -14x = 0 9.8 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.96 + -2.8x + x2 = 0 Move the constant term to the right: Add '-1.96' to each side of the equation. 1.96 + -2.8x + -1.96 + x2 = 0 + -1.96 Reorder the terms: 1.96 + -1.96 + -2.8x + x2 = 0 + -1.96 Combine like terms: 1.96 + -1.96 = 0.00 0.00 + -2.8x + x2 = 0 + -1.96 -2.8x + x2 = 0 + -1.96 Combine like terms: 0 + -1.96 = -1.96 -2.8x + x2 = -1.96 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 = -1.96 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = -1.96 + 1.96 Combine like terms: -1.96 + 1.96 = 0.00 1.96 + -2.8x + x2 = 0.00 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -1.4) equal to 0.00 and 0.00.Subproblem 1
x + -1.4 = 0.00 Simplifying x + -1.4 = 0.00 Reorder the terms: -1.4 + x = 0.00 Solving -1.4 + x = 0.00 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 = 0.00 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 0.00 + 1.4 x = 0.00 + 1.4 Combine like terms: 0.00 + 1.4 = 1.4 x = 1.4 Simplifying x = 1.4Subproblem 2
x + -1.4 = 0.00 Simplifying x + -1.4 = 0.00 Reorder the terms: -1.4 + x = 0.00 Solving -1.4 + x = 0.00 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 = 0.00 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 0.00 + 1.4 x = 0.00 + 1.4 Combine like terms: 0.00 + 1.4 = 1.4 x = 1.4 Simplifying x = 1.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4, 1.4}
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