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Simplifying 28x2 + 34x + 7 = 0 Reorder the terms: 7 + 34x + 28x2 = 0 Solving 7 + 34x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.25 + 1.214285714x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.214285714x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.214285714x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.214285714x + x2 = 0 + -0.25 1.214285714x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.214285714x + x2 = -0.25 The x term is 1.214285714x. Take half its coefficient (0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. 1.214285714x + 0.3686224488 + x2 = -0.25 + 0.3686224488 Reorder the terms: 0.3686224488 + 1.214285714x + x2 = -0.25 + 0.3686224488 Combine like terms: -0.25 + 0.3686224488 = 0.1186224488 0.3686224488 + 1.214285714x + x2 = 0.1186224488 Factor a perfect square on the left side: (x + 0.607142857)(x + 0.607142857) = 0.1186224488 Calculate the square root of the right side: 0.344416098 Break this problem into two subproblems by setting (x + 0.607142857) equal to 0.344416098 and -0.344416098.Subproblem 1
x + 0.607142857 = 0.344416098 Simplifying x + 0.607142857 = 0.344416098 Reorder the terms: 0.607142857 + x = 0.344416098 Solving 0.607142857 + x = 0.344416098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + x = 0.344416098 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = 0.344416098 + -0.607142857 x = 0.344416098 + -0.607142857 Combine like terms: 0.344416098 + -0.607142857 = -0.262726759 x = -0.262726759 Simplifying x = -0.262726759Subproblem 2
x + 0.607142857 = -0.344416098 Simplifying x + 0.607142857 = -0.344416098 Reorder the terms: 0.607142857 + x = -0.344416098 Solving 0.607142857 + x = -0.344416098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.607142857' to each side of the equation. 0.607142857 + -0.607142857 + x = -0.344416098 + -0.607142857 Combine like terms: 0.607142857 + -0.607142857 = 0.000000000 0.000000000 + x = -0.344416098 + -0.607142857 x = -0.344416098 + -0.607142857 Combine like terms: -0.344416098 + -0.607142857 = -0.951558955 x = -0.951558955 Simplifying x = -0.951558955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.262726759, -0.951558955}
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