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Simplifying x + x + 7 = 78x2 Reorder the terms: 7 + x + x = 78x2 Combine like terms: x + x = 2x 7 + 2x = 78x2 Solving 7 + 2x = 78x2 Solving for variable 'x'. Combine like terms: 78x2 + -78x2 = 0 7 + 2x + -78x2 = 0 Begin completing the square. Divide all terms by -78 the coefficient of the squared term: Divide each side by '-78'. -0.08974358974 + -0.02564102564x + x2 = 0 Move the constant term to the right: Add '0.08974358974' to each side of the equation. -0.08974358974 + -0.02564102564x + 0.08974358974 + x2 = 0 + 0.08974358974 Reorder the terms: -0.08974358974 + 0.08974358974 + -0.02564102564x + x2 = 0 + 0.08974358974 Combine like terms: -0.08974358974 + 0.08974358974 = 0.00000000000 0.00000000000 + -0.02564102564x + x2 = 0 + 0.08974358974 -0.02564102564x + x2 = 0 + 0.08974358974 Combine like terms: 0 + 0.08974358974 = 0.08974358974 -0.02564102564x + x2 = 0.08974358974 The x term is -0.02564102564x. Take half its coefficient (-0.01282051282). Square it (0.0001643655490) and add it to both sides. Add '0.0001643655490' to each side of the equation. -0.02564102564x + 0.0001643655490 + x2 = 0.08974358974 + 0.0001643655490 Reorder the terms: 0.0001643655490 + -0.02564102564x + x2 = 0.08974358974 + 0.0001643655490 Combine like terms: 0.08974358974 + 0.0001643655490 = 0.089907955289 0.0001643655490 + -0.02564102564x + x2 = 0.089907955289 Factor a perfect square on the left side: (x + -0.01282051282)(x + -0.01282051282) = 0.089907955289 Calculate the square root of the right side: 0.299846553 Break this problem into two subproblems by setting (x + -0.01282051282) equal to 0.299846553 and -0.299846553.Subproblem 1
x + -0.01282051282 = 0.299846553 Simplifying x + -0.01282051282 = 0.299846553 Reorder the terms: -0.01282051282 + x = 0.299846553 Solving -0.01282051282 + x = 0.299846553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01282051282' to each side of the equation. -0.01282051282 + 0.01282051282 + x = 0.299846553 + 0.01282051282 Combine like terms: -0.01282051282 + 0.01282051282 = 0.00000000000 0.00000000000 + x = 0.299846553 + 0.01282051282 x = 0.299846553 + 0.01282051282 Combine like terms: 0.299846553 + 0.01282051282 = 0.31266706582 x = 0.31266706582 Simplifying x = 0.31266706582Subproblem 2
x + -0.01282051282 = -0.299846553 Simplifying x + -0.01282051282 = -0.299846553 Reorder the terms: -0.01282051282 + x = -0.299846553 Solving -0.01282051282 + x = -0.299846553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01282051282' to each side of the equation. -0.01282051282 + 0.01282051282 + x = -0.299846553 + 0.01282051282 Combine like terms: -0.01282051282 + 0.01282051282 = 0.00000000000 0.00000000000 + x = -0.299846553 + 0.01282051282 x = -0.299846553 + 0.01282051282 Combine like terms: -0.299846553 + 0.01282051282 = -0.28702604018 x = -0.28702604018 Simplifying x = -0.28702604018Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31266706582, -0.28702604018}
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