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Simplifying 5x2 + 6x = 13 Reorder the terms: 6x + 5x2 = 13 Solving 6x + 5x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 6x + 5x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 1.2x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 1.2x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 1.2x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 1.2x + x2 = 0 + 2.6 1.2x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 1.2x + x2 = 2.6 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 2.6 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 2.6 + 0.36 Combine like terms: 2.6 + 0.36 = 2.96 0.36 + 1.2x + x2 = 2.96 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 2.96 Calculate the square root of the right side: 1.720465053 Break this problem into two subproblems by setting (x + 0.6) equal to 1.720465053 and -1.720465053.Subproblem 1
x + 0.6 = 1.720465053 Simplifying x + 0.6 = 1.720465053 Reorder the terms: 0.6 + x = 1.720465053 Solving 0.6 + x = 1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 1.720465053 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.720465053 + -0.6 x = 1.720465053 + -0.6 Combine like terms: 1.720465053 + -0.6 = 1.120465053 x = 1.120465053 Simplifying x = 1.120465053Subproblem 2
x + 0.6 = -1.720465053 Simplifying x + 0.6 = -1.720465053 Reorder the terms: 0.6 + x = -1.720465053 Solving 0.6 + x = -1.720465053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -1.720465053 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.720465053 + -0.6 x = -1.720465053 + -0.6 Combine like terms: -1.720465053 + -0.6 = -2.320465053 x = -2.320465053 Simplifying x = -2.320465053Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.120465053, -2.320465053}
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