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Simplifying 3x2 + 1 + -7x = 13x2 Reorder the terms: 1 + -7x + 3x2 = 13x2 Solving 1 + -7x + 3x2 = 13x2 Solving for variable 'x'. Combine like terms: 3x2 + -13x2 = -10x2 1 + -7x + -10x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 1 + -7x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.1 + 0.7x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.7x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.7x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.7x + x2 = 0.0 + 0.1 0.7x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 0.7x + x2 = 0.1 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = 0.1 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 0.1 + 0.1225 Combine like terms: 0.1 + 0.1225 = 0.2225 0.1225 + 0.7x + x2 = 0.2225 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 0.2225 Calculate the square root of the right side: 0.471699057 Break this problem into two subproblems by setting (x + 0.35) equal to 0.471699057 and -0.471699057.Subproblem 1
x + 0.35 = 0.471699057 Simplifying x + 0.35 = 0.471699057 Reorder the terms: 0.35 + x = 0.471699057 Solving 0.35 + x = 0.471699057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.471699057 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.471699057 + -0.35 x = 0.471699057 + -0.35 Combine like terms: 0.471699057 + -0.35 = 0.121699057 x = 0.121699057 Simplifying x = 0.121699057Subproblem 2
x + 0.35 = -0.471699057 Simplifying x + 0.35 = -0.471699057 Reorder the terms: 0.35 + x = -0.471699057 Solving 0.35 + x = -0.471699057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.471699057 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.471699057 + -0.35 x = -0.471699057 + -0.35 Combine like terms: -0.471699057 + -0.35 = -0.821699057 x = -0.821699057 Simplifying x = -0.821699057Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.121699057, -0.821699057}
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