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Simplifying 10x2 = 13 + 2x Solving 10x2 = 13 + 2x Solving for variable 'x'. Reorder the terms: -13 + -2x + 10x2 = 13 + 2x + -13 + -2x Reorder the terms: -13 + -2x + 10x2 = 13 + -13 + 2x + -2x Combine like terms: 13 + -13 = 0 -13 + -2x + 10x2 = 0 + 2x + -2x -13 + -2x + 10x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -13 + -2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.3 + -0.2x + x2 = 0 Move the constant term to the right: Add '1.3' to each side of the equation. -1.3 + -0.2x + 1.3 + x2 = 0 + 1.3 Reorder the terms: -1.3 + 1.3 + -0.2x + x2 = 0 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + -0.2x + x2 = 0 + 1.3 -0.2x + x2 = 0 + 1.3 Combine like terms: 0 + 1.3 = 1.3 -0.2x + x2 = 1.3 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 1.3 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 1.3 + 0.01 Combine like terms: 1.3 + 0.01 = 1.31 0.01 + -0.2x + x2 = 1.31 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 1.31 Calculate the square root of the right side: 1.144552314 Break this problem into two subproblems by setting (x + -0.1) equal to 1.144552314 and -1.144552314.Subproblem 1
x + -0.1 = 1.144552314 Simplifying x + -0.1 = 1.144552314 Reorder the terms: -0.1 + x = 1.144552314 Solving -0.1 + x = 1.144552314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.144552314 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.144552314 + 0.1 x = 1.144552314 + 0.1 Combine like terms: 1.144552314 + 0.1 = 1.244552314 x = 1.244552314 Simplifying x = 1.244552314Subproblem 2
x + -0.1 = -1.144552314 Simplifying x + -0.1 = -1.144552314 Reorder the terms: -0.1 + x = -1.144552314 Solving -0.1 + x = -1.144552314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.144552314 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.144552314 + 0.1 x = -1.144552314 + 0.1 Combine like terms: -1.144552314 + 0.1 = -1.044552314 x = -1.044552314 Simplifying x = -1.044552314Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.244552314, -1.044552314}
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