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Simplifying 25x2 + 14x + -70 = 0 Reorder the terms: -70 + 14x + 25x2 = 0 Solving -70 + 14x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.8 + 0.56x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 0.56x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 0.56x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 0.56x + x2 = 0 + 2.8 0.56x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 0.56x + x2 = 2.8 The x term is 0.56x. Take half its coefficient (0.28). Square it (0.0784) and add it to both sides. Add '0.0784' to each side of the equation. 0.56x + 0.0784 + x2 = 2.8 + 0.0784 Reorder the terms: 0.0784 + 0.56x + x2 = 2.8 + 0.0784 Combine like terms: 2.8 + 0.0784 = 2.8784 0.0784 + 0.56x + x2 = 2.8784 Factor a perfect square on the left side: (x + 0.28)(x + 0.28) = 2.8784 Calculate the square root of the right side: 1.696584805 Break this problem into two subproblems by setting (x + 0.28) equal to 1.696584805 and -1.696584805.Subproblem 1
x + 0.28 = 1.696584805 Simplifying x + 0.28 = 1.696584805 Reorder the terms: 0.28 + x = 1.696584805 Solving 0.28 + x = 1.696584805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28' to each side of the equation. 0.28 + -0.28 + x = 1.696584805 + -0.28 Combine like terms: 0.28 + -0.28 = 0.00 0.00 + x = 1.696584805 + -0.28 x = 1.696584805 + -0.28 Combine like terms: 1.696584805 + -0.28 = 1.416584805 x = 1.416584805 Simplifying x = 1.416584805Subproblem 2
x + 0.28 = -1.696584805 Simplifying x + 0.28 = -1.696584805 Reorder the terms: 0.28 + x = -1.696584805 Solving 0.28 + x = -1.696584805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28' to each side of the equation. 0.28 + -0.28 + x = -1.696584805 + -0.28 Combine like terms: 0.28 + -0.28 = 0.00 0.00 + x = -1.696584805 + -0.28 x = -1.696584805 + -0.28 Combine like terms: -1.696584805 + -0.28 = -1.976584805 x = -1.976584805 Simplifying x = -1.976584805Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.416584805, -1.976584805}
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