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Simplifying 21x2 + -78x + 49 = 0 Reorder the terms: 49 + -78x + 21x2 = 0 Solving 49 + -78x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 2.333333333 + -3.714285714x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -3.714285714x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -3.714285714x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -3.714285714x + x2 = 0 + -2.333333333 -3.714285714x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -3.714285714x + x2 = -2.333333333 The x term is -3.714285714x. Take half its coefficient (-1.857142857). Square it (3.448979591) and add it to both sides. Add '3.448979591' to each side of the equation. -3.714285714x + 3.448979591 + x2 = -2.333333333 + 3.448979591 Reorder the terms: 3.448979591 + -3.714285714x + x2 = -2.333333333 + 3.448979591 Combine like terms: -2.333333333 + 3.448979591 = 1.115646258 3.448979591 + -3.714285714x + x2 = 1.115646258 Factor a perfect square on the left side: (x + -1.857142857)(x + -1.857142857) = 1.115646258 Calculate the square root of the right side: 1.056241572 Break this problem into two subproblems by setting (x + -1.857142857) equal to 1.056241572 and -1.056241572.Subproblem 1
x + -1.857142857 = 1.056241572 Simplifying x + -1.857142857 = 1.056241572 Reorder the terms: -1.857142857 + x = 1.056241572 Solving -1.857142857 + x = 1.056241572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = 1.056241572 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = 1.056241572 + 1.857142857 x = 1.056241572 + 1.857142857 Combine like terms: 1.056241572 + 1.857142857 = 2.913384429 x = 2.913384429 Simplifying x = 2.913384429Subproblem 2
x + -1.857142857 = -1.056241572 Simplifying x + -1.857142857 = -1.056241572 Reorder the terms: -1.857142857 + x = -1.056241572 Solving -1.857142857 + x = -1.056241572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = -1.056241572 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = -1.056241572 + 1.857142857 x = -1.056241572 + 1.857142857 Combine like terms: -1.056241572 + 1.857142857 = 0.800901285 x = 0.800901285 Simplifying x = 0.800901285Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.913384429, 0.800901285}
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