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Simplifying 5x2 + 7x = 21 Reorder the terms: 7x + 5x2 = 21 Solving 7x + 5x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + 7x + 5x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + 1.4x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 1.4x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 1.4x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 1.4x + x2 = 0 + 4.2 1.4x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 1.4x + x2 = 4.2 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 4.2 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 4.2 + 0.49 Combine like terms: 4.2 + 0.49 = 4.69 0.49 + 1.4x + x2 = 4.69 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 4.69 Calculate the square root of the right side: 2.165640783 Break this problem into two subproblems by setting (x + 0.7) equal to 2.165640783 and -2.165640783.Subproblem 1
x + 0.7 = 2.165640783 Simplifying x + 0.7 = 2.165640783 Reorder the terms: 0.7 + x = 2.165640783 Solving 0.7 + x = 2.165640783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 2.165640783 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 2.165640783 + -0.7 x = 2.165640783 + -0.7 Combine like terms: 2.165640783 + -0.7 = 1.465640783 x = 1.465640783 Simplifying x = 1.465640783Subproblem 2
x + 0.7 = -2.165640783 Simplifying x + 0.7 = -2.165640783 Reorder the terms: 0.7 + x = -2.165640783 Solving 0.7 + x = -2.165640783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -2.165640783 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -2.165640783 + -0.7 x = -2.165640783 + -0.7 Combine like terms: -2.165640783 + -0.7 = -2.865640783 x = -2.865640783 Simplifying x = -2.865640783Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.465640783, -2.865640783}
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