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Simplifying 5x2 + 7x + -35 = 0 Reorder the terms: -35 + 7x + 5x2 = 0 Solving -35 + 7x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7 + 1.4x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 1.4x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 1.4x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 1.4x + x2 = 0 + 7 1.4x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 1.4x + x2 = 7 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 = 7 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 7 + 0.49 Combine like terms: 7 + 0.49 = 7.49 0.49 + 1.4x + x2 = 7.49 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 7.49 Calculate the square root of the right side: 2.736786437 Break this problem into two subproblems by setting (x + 0.7) equal to 2.736786437 and -2.736786437.Subproblem 1
x + 0.7 = 2.736786437 Simplifying x + 0.7 = 2.736786437 Reorder the terms: 0.7 + x = 2.736786437 Solving 0.7 + x = 2.736786437 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 = 2.736786437 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 2.736786437 + -0.7 x = 2.736786437 + -0.7 Combine like terms: 2.736786437 + -0.7 = 2.036786437 x = 2.036786437 Simplifying x = 2.036786437Subproblem 2
x + 0.7 = -2.736786437 Simplifying x + 0.7 = -2.736786437 Reorder the terms: 0.7 + x = -2.736786437 Solving 0.7 + x = -2.736786437 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 = -2.736786437 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -2.736786437 + -0.7 x = -2.736786437 + -0.7 Combine like terms: -2.736786437 + -0.7 = -3.436786437 x = -3.436786437 Simplifying x = -3.436786437Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.036786437, -3.436786437}
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